electrostatics 2014

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“It’s not that I am so smart it’s just that I stay with problems longer Albert EinsteinElectrostatics Unit I: Electrostatics Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in uniform electric field. Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator. [1993] Q.1 Calculate the electric field between two metal plates 3 man apart connected to a 2V battery. Q.2 If an oil drop of weight 3.2 10 -13 N balanced in an electric field of strength 5 10 5 V/m, find the charge on the oil drop. [1994] CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES (1) PHYSICS AURORA CLASSES E = mc 2

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Page 1: Electrostatics 2014

“It’s not that I am so smart it’s just that I stay with problems longer Albert Einstein”

Electrostatics

Unit I: Electrostatics

Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution.

Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in uniform electric field.

Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).

Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.

Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator.

[1993]Q.1 Calculate the electric field between two metal plates 3 man apart connected to a 2V battery.

Q.2 If an oil drop of weight 3.2 10-13 N balanced in an electric field of strength 5 105 V/m, find the charge on the oil drop.

[1994]Q.1 (a) Write Coulomb’s law in vector form. (b) Find the electric field intensity at a point at a distance r

from a charge of q coulomb in space.

Q.2 Write two uses of a capacitor.

Q.3 Calculate the distance between two protons such that the electric force between them is equal to the weight of either.

[1996]Q.1 What is the work done in moving a charge of 10 nC between two points on an equipotential surface?

Q.2 An electric dipole, when held at 30 with respect to a uniform electric field of 104 N/C, experiences a torque of 9 10-26 Nm. Calculate the dipole moment of the dipole.

Q.3 In a parallel plate capacitor, the capacitance increases from 4 microfarad to 80 microfarad, on introducing a dielectric medium between the plates. What is the dielectric constant of the medium?

Q.4 The electric field at a point due to a point charge is 20 N/C and the electric potential at that point is 10 J/C. Calculate the distance of the point from the charge and the magnitude of the charge.

[1997]CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(1)

PHYSICSAURORA CLASSES

E = mc2

Page 2: Electrostatics 2014

Q.1 Force between two point electric charges kept at a distance d apart in air is F. If these charges are kept at the same distance in water, how does the force between them change?

Q.2 Two point electric charges of unknown magnitude and sign are placed a distance ‘d’ apart. The electric field intensity is zero at a point, not between the charges but on the line joining them. Write two essential conditions for this to happen.

Q.3 Define ‘dielectric constant’ of a medium in terms of force between electric charges.

[1998]Q.1 Two protons A and B are placed between two parallel plates having a potential difference V as shown

in the figure

Will these experience equal or unequal force?

Q.2 An electric dipole is held in field.

(i) Show that no translatory force acts on it.

(ii) Derive an expression for the torque acting on it.

Q.3 In a medium the force of attraction between two point electric charges, distance ‘d’ apart, is F. What distance apart should these be kept in the same medium so that the force between them becomes 3F?

[1999]Q.1 Draw an equipotential surface in a uniform electric field.

Q.2 Define dipole moment of an electric dipole. Show mathematically that the electric field intensity due to a short dipole at a distance ‘d’ along its axis is twice the intensity at the same distance along the equatorial axis.

OrExplain the principle, construction and working of A Van de Graft generator.

[2000]

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(2)

+

+

+

+

+

B

o

A

o

V

EuipotentialSurface

E

Page 3: Electrostatics 2014

Q.1 An electric dipole of length 2 cm is placed with its axis making an angular 60 to a uniform electric field of 105 N/C. If it experiences a torque of 83 Nm. Calculate the

(i) magnitude of the charge on the dipole, and

(ii) potential energy of the dipole.

Q.2 Two charged spherical conductors, each of radius R, are distant d (>2 R). They carry charger +q and –1. Will the force of attraction between them be exactly q2/4p 0d2?

Q.3 In an electric field an electron is kept freely. If the electron is replaced by a proton, what will be the relationship between the forces experienced by them?

Q.4 Give the S.I. unit of electric field intensity. Is electric field intensity a scalar or a vector quantity?

Q.5 Two point charges A and B of value + 5 10-9 C and + 3 10-9 C are kept 6 cm apart in air. Calculate the work done when charge B is moved by 1 cm towards charge A.

Q.6 Define the term ‘electric field intensity’. Electric field inside a conductor is zero. Explain.

[2001]Q.1 What does q1 + q2 = 0 signify in electrostatics? Q.2 What orientation of an electric dipole in uniform electric field corresponds to its stable equilibrium? Q.3 What should be the work done if a point charge +q is taken from a point A to the point B on the

circumference drawn with another point +q at the center? Q.4 A and B are two conducting spheres of the same radius, A being solid and B hollow. Both are charged

to the same potential. What will be the relation between the charges on the two spheres? Q.5 What is equipotential surface? Show that electric field is always directed perpendicular to

equipotential surface. Q.6 The force of attraction between two point charges placed at a distance‘d’ apart in a medium is F. What

should be the distance apart in the same medium so that the force of attraction between them becomes F/4.

Q.7 Use Gauss theorem to find the value of electric field intensity at a point inside a hollow charged conducting sphere.

Q.8 Show that the energy stored in a parallel plate capacitor is ½ CV2. Hence derive an expression for the energy density of a capacitor.

Q.9 Two point charges of + 5 10-19 C and + 20 10-19 C are separated by a distance of 2m. Find the point on the line joining them at which electric field intensity is zero.

Q.10 A uniform electric filed exists between two charged plates at shown in fig. What should be the work done in moving a charge q along the closed rectangular path ABCD.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(3)

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Page 4: Electrostatics 2014

[2002]Q.1 Which physical quantity has unit NC-1? Is it a vector or a scalar quantity? Q.2 Express dielectric constant in terms of capacitance. Q.3 What is the function of a dielectric in a capacitor? Q.4 How much work is done in moving a 500 C charge between two points on an equipotential surface? Q.5 Find an expression for the maximum torque acting on an electric dipole when it is placed in a uniform

electric field. Q.6 Two identical metallic spheres, having unequal opposite charges are placed at a distance of 0.50 m

apart in air. After bringing them in contact with each other, they are again placed at the same distance apart. Now the force of repulsion between them is 0.108 N. Calculate the final charge on each of them.

Q.7 A steam of electrons traveling with speed m/s at right angles to a uniform electric field E is deflected in a circular path of radius r Prove that

E/m = 2/rE Q.8 Find the equivalent capacitance of the combination of capacitors between the points A and B as shown

in fig. Also calculate the total charge that flows in the circuit when a 100 V battery is connected between the points A and B.

[2003]Q.1 Write S.I. unit of (i) electric field intensity and (ii) electric dipole moment. Q.2 What is an equipotential surface? Q.3 Two point charge qA = + 3C and qB = - 3C are located points A and B 20 cm apart in vacuum. (i)

Find the electric field at the mid point of the line AB joining the two charges. (ii) If a negative test charge of magnitude 1.5 10-9 C is placed at the centre, find the force experience by the test charges.

[2004]Q.1 An electric dipole with moment p is placed in a uniform electric field of intensity E. Write the

expression for the torque experienced by the dipole. Identify two pairs of perpendicular vectors in the expression.

Q.2 The distance of the field point, on the equatorial plane of a small electric dipole is halved. By what factor does the electric filed due to the dipole change?

Q.3 The distance of the field point on the axis of a small dipole is doubled. By what factor will the electric filed, due to the dipole change?

Q.4 Name the dielectric whose molecules have (i) non-zero and (ii) zero dipole moment. Q.5 Define dielectric constant of a medium. What is the value of dielectric constant for a metal? Q.6 The graph shows the variation of voltage ‘V’ across the plates of two capacitors A and B versus

increase of charge ‘Q’ stored on them. Which of the two capacitors has higher capacitance? Give reason for your answer.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(4)

Page 5: Electrostatics 2014

Q.7 State Gauss Theorem in electrostatics. Using this theorem derive the expression for the electric field intensity at a point outside a uniformly charged thin spherical shell.

Q.8 Briefly explain the principle of a capacitor. Derive an expression for the capacitance of a parallel plate capacitor, whose plates are separated by a dielectric medium.

Q.9 Two point charges 10 10-8 C and – 4 10-8 C are separated by a distance of 70 cm in air as shown in figure. (i) Find at what distance from point. A would the electric potential be zero.(ii) Also calculate the electrostatic potential energy of the system.

Q.10 The flux of electrostatic field through the closed spherical surface S’ is found to be four times that through the closed spherical surface S. Find the magnitude of the charge Q. Given q1 = 1C, q2 = 2C, q3 = 9.84C.

Q.11 X and Y are two parallel plate capacitors having the same areas of plates and same separation between the plates. X has air between the plates and Y contains at dielectric medium r = 5.(i) Calculate the p potential difference between the plates of X and Y.(ii) What is the ratio of electrostatic energy stored in X and Y?

Q.12 Two charges + 10 C and - 10 C are separated by a distance of 40 cm in air. (i) Calculate the electrostatic potential energy of the system, assuming zero potential energy at infinity (ii) Draw an equipotential surface of the system.

Q.13 Find the total energy stored in the capacitors in the given network :

Q.14 An electric dipole of length 8 cm, when placed with its axes making an angle of 60 , with a uniform electric field experiences a torque of 83 N-m. Calculate the (i) magnitude of electric field (ii) potential energy of dipole; if the dipole has charge 4 nC.

Q.15 20 F capacitor is charged by a 30 V dc supply and then connected across an uncharged 50 F capacitor. Calculate (i) the final potential difference across the combination and (ii) the initial and final energies. How will you account for the difference in energy?

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(5)

B

AV

Q

70 cm

10 10-8 C – 4 10-8 C

X Y

12 V

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2F

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Page 6: Electrostatics 2014

[2005]Q.1 Which physical quantity has its SI unit as?

(i) C – m (ii) Vm

Q2. Three charges -2 C, 22 C and - 2 C are arranged along a straight line as shown in figure.

Calculate the total electric field intensity due to all these three charges at the point ‘P’.

Q.3 How does the electric field inside a dielectric decrease when it is placed in an external electric field?

Q.4 An electric dipole is held in an uniform electric field (i) using suitable diagram show that it done not undergo any translatory motion, and (ii) derive an expression for torque acting on it and specify its direction.

Q.5 State Gauss Theorem. Apply this theorem to obtain the expression for the electric field at a point due to an in infinitely long, thin uniformly charged straight wire.

Q.6 Two capacitors, of capacitance 3F and 6F, are charged to potentials of 2V and 5V respectively. These two charged capacitors are connected in series. Find the potential across each of the two capacitors now?

Q.7 Obtain an expression for the energy stored in a parallel plate capacitor. In the following figure, the energy stored in C4 is 27J? Calculate the total energy stored in the system.

3

ORState the theorem, which relates the enclosed charge, inside a closed surface, with the electric flux through it. Use this theorem to obtain the electric field due to a uniformly charged thin spherical shell at an

(i) outside point(ii) inside point.

An electric charge of 8.85 10-13C is placed at the centre of a sphere of radius 1m. What is the total electric flux linked with the sphere? How will the electric flux change if another equal and opposite charge in introduced at a distance of

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(6)

1 m

P

B

1m 1 m

-2C 22C -2C

A C

P

1 f

C1 Q

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Page 7: Electrostatics 2014

(i) 0.5m form the centre (ii) 1.5m from the centre

Q.8 The electric field lines never cross each other, why?Q.9 An electrostatic field line cannot be discontinuous, why?Q.10 An electric dipole of moment 20 10-6 C is enclosed by closed surface. What is the net electric flux

coming out of this surface?Q.11 Define electric line of force and give its two important properties.Q.12 Define electric field intensity. Write its S.I. unit. Write the magnitude and direction of electric field

intensity due to an electric dipole of length 2a at the mid point of the line joining the two charges. Q.13 A small metal sphere carrying charge + Q is located at the centre of a spherical cavity in a large

uncharged metal sphere as shown in fig. Use Gauss’s theorem to find electric field at points P1 and P2.

Q.14 A charge q is placed at the centre of the line joining two equal charges Q. Show that the system of

three charges will be in equilibrium of

Q.15 A parallel plate capacitor is to be designed with a voltage rating 1 kV using a material of dielectric constant 3 and dielectric strength 107 Vm-1. For safety we would like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50 pF?

Q.16 A 4 F capacitor is charged by a 200 V supply. The supply is then disconnected and the charged capacitor is connected to another uncharged 2 F capacitor. How much electrostatic energy of the first capacitor is lost in the process of attaining the steady situation?

[2006]Q.1 An electric dipole of length 10 cm having charges 6 10-3 C, plated at 30 with respect to uniform

electric filed, experiences a torques of magnitude 63 Nm. Calculate (i) the magnitude of the electric field (ii) the potential energy of the dipole.

Q.2 Define electric flux. Write its S.I. Units. Using Gauss theorem, derive an expression for the electric filed intensity at any point outside a charged spherical shell.

Q.3 Derive the expression for the energy stored in a parallel plate capacitor with air between the plates. How does the stored energy change if air is replaced by a medium of dielectric constant K?

Q.4 Define the terms electric dipole and dipole moment? Derive an expression for the electric field at a point of equatorial line of dipole?

ORWith the help of a labelled diagram, explain the working of a Van De Graff generator. Mention its use?

Q.5 A point charge q is placed at O as show in fug. Is VP –VQ is positive or negative when (i) q > 0 (ii) q < 0. Justify your answer.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(7)

Metal

Free space+Q

P1P2

r2r1

P

O Q

P

Page 8: Electrostatics 2014

Q.6 The given graph shows the variation of charge q versus potential difference V for capacitors C 1 and C2. The two capacitors have same plate separation, but the plate area of C2 is double than that of C1. Which of the lines in the graph correspond to C1 and C2 and why?

Q.7 Two capacitor of capacitance 6F and 12F are connected in series with a battery. The voltage across the 6F capacitors is 2V. Compute the total battery voltage.

Q.8 Express dielectric constant in terms of capacitance.Q.9 Define electric dipole moment. Is it a scalar or a vector quantity?

[2007]Q.1 Two point charges 4C and - 2C are separated by a distance of 1 m in air. Calculate at what point on

the line joining the two charges is the electric potential zero. Q.2 State Gauss’s theorem in electrostatics. Apply this theorem to derive an expression for electric field

intensity at a point near an infinitely long straight charged wire. Q.3 Explain the underlying of working of a parallel plate capacitor.

If two similar plates, each of area A having surface charge densities + and - are separated by a distance d in air, write expression for (i) the electric field at points between the two plates.(ii) the potential difference between the plates.(iii) The capacitance of the capacitor so formed.

Q.4 Derive expression for the electric potential due to an electric dipole at any point on its axis. Mention are contrasting feature of electric potential of a dipole at a point as compared to that due to a signal charge.

Q.5 The force acting between two point charges q1 and q2 kept at some distance apart in air is attractive or repulsive when (i) q1 q2 > 0 (i) q1q2 < 0.

Q.6 Define electric flux. Write its S.I. unit. A spherical rubber balloon carries a charge that is uniformly distributed over its surface. As the balloon is blown up and increases in size, how does the total electric flux coming out of the surface charge? Give reason.

Q.7 A parallel plate capacitor each with plate area A and separation‘d’ is charged to a potential difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric constant K is placed between the plates. What change if any, will take place in (i) charge on the plates (ii) electric field intensity between the plates,(iii) capacitor of the capacitor Justify your answer in each case.

Q.8 (i) Using Gauss Theorem show mathematically that for any point outside the shell, the field due to a uniformly charged spherical shell is same as the entire charged shell is connected at the centre.

(ii) Why do you expect the electric field inside the shell to be zero according to this theorem?

[2008]Q.1 Which orientation of an electric dipole in a uniform electric field would correspond to stable

equilibrium? CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(8)

A

BQ

V

Page 9: Electrostatics 2014

Q.2 Two point charges, q1 = 10 10-8C and q2 = -2 10-8 C are separated by a distance of 60 cm in air.(i) Find at what distance from the Ist charge, q1 would the electric potential be zero.(ii) Also calculate the electrostatic potential energy of the system.

OrTwo point 4Q, Q are separated by 1m in air. At what point on the line the charge is the electric field intensity zero? Also calculate the electrostatics potential energy of the system of charges, taking the value of charge, Q = 2 10-7 C.

Q.3 Derive an expression for the energy stored in a parallel plate capacitor.On charging, a parallel plate capacitor to a potential plate V, the spacing between the plates is halved, and a dielectric medium of r = 10 is introduced between the plates, without disconnecting the d.c. source. Explain, using suitable expressions, how the (i) capacitance, (ii) electric field and (iii) energy density of the capacitor change.

Or(a) Define electric flux. Write its SI units.(b) The electric field components due to a charge inside the cube of side 0.1 m are as shown:

Ex = x, where = 500 N/c-m

Ey = 0, Ez = 0

Calculate (i) the flux through the cube and (ii) the charge inside the cube.

Q.4 Draw an equipotential surface for a system consisting of two charges Q, -Q separated by a distance r in air.

Q.5 A 500 C charges is at the center of a square of side 10 cm. Find the work done in moving the charge of 10 C between two diagonally opposite points on the square.

Q.6 Draw the electric field lines due to a uniformly charged thin spherical shell when charge on the shell is (i) positive and (ii) negative.

Q.7 Calculate the work done to dissociate the system of three charges placed on the vertices of a triangle as shown q = 1.6 10-10C

Q.8 A uniformly charged conducting sphere of diameter 2.5 m has a surface charged density 100 C/m2.

Q.9 Obtain the equivalent capacitance of the network given below. For a supply of 300 V, determine the charge and voltage across C4.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(9)

y

O

z

0.1m 0.1

m

x

B

A

O

q500 C

Page 10: Electrostatics 2014

Q.10 A Van de Graff type generator is capable of building up potential difference of 15 106V. The dielectric strength of the gas surrounding the electrode is 5 107Vm-1? What is the minimum radius of the spherical shell required?

[2009]Q.1 Define the term 'potential energy' of charge 'q' at a distance 'r' in an external electric field. [1]

Q.2 A positive point charge (+q) is kept in the vicinity of an uncharged conducting plate. Sketch electric field lines originating from the point on to the surface of the plate.Derive the expression for the electric field at the surface of a charged conductor. [3]

OrA parallel plate capacitor is charged by a battery. Meter some time the battery is disconnected and a dielectric slab of dielectric constant K is inserted between the plates. How would (i) the capacitance, (ii) the electric field between the plates and (iii) the energy stored in the capacitor, be affected? Justify your answer. [3]

[2010]Q.1 Name the physical quantity whose S.I. unit is JC-1. Is it a scalar or a vector quantity? [1]

Q.2 A network of four capacitors each of 12 F capacitance is connected to a 500 V supply as shown in the figure. Determine (a) equivalent capacitance of the netweork and (b) charge on each capacitor. [3]

Q.3 A spherical conducting shell of inner radius r1 and outer radius r2 has a charge ‘Q’ A charge ‘q’ is placed at the centre of the shell.(a) What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell?

(b) Write the expression for the electric field at a point x > x2 from the centre of the shell. [2]

Q.4 Show that the electric field at the surface of a charged conductor is given by where is the

surface charge density and is a unit vector normal to the surface in the outward direction. [2]

[2011]Q.1 Define electric dipole moment. Write its S.I. unit. [1]

Q.2 A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. What is the potential at the centre of the sphere? [1]

Q.3 A thin straight infinitely long conducting wire having charge density is enclosed by a cylindrical surface of radius r and length , its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder. [2]

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(10)

Page 11: Electrostatics 2014

Q.4 Plot a graph showing the variation of coulomb force (F) versus (1/r2), where r is the distance between the two charges of each pair of charges : (1C, 2C,) and (2C, -3C,). Interpret the graphs obtained. [2]

Q.5 A parallel plate capacitor is being charged by a time varying current. Explain briefly how Ampere’s circuital law is generalized to incorporate the effect due to the displacement current. [2]

Q.6 Net capacitance of three identical capacitors in series is 1F. What will be their net capacitance if connected in parallel? Find the ratio of energy stored in the two configurations if they are both connected to the same source.

[2]

[2012]Q.1 A charge ‘q’ is placed at the centre of the cube of side .What is the electric flux passing through two

opposite faces of the cubes? [1]

Q.2 A capacitor of capacitance ‘C’ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor. [2]

Q.3 A test charge ‘q’ is moved without acceleration from A to C along the path from A to B and then from B to C in electric field E as shown in the figure. (i) Calculate the potential difference between A and C. (ii) At which point (of the two) is the electric potential more and why? [2]

Q.4 An electric dipole is held in a uniform electric field.(i) Show that the net force acting on it is zero.(ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of

180. [2]Q.5 Deduce the expression for the electrostatic energy stored in a capacitor of capacitance ‘C’ and having

charge ‘Q’How will the (i) energy stored and (ii) electric field inside the capacitor be affected when it is completely filled with a dielectric material of dielectric constant ‘K’? [3]

[2013]Q.1 A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate

capacitor but has the thickness d/3, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.

Q.2 A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(11)

Page 12: Electrostatics 2014

Q.3 (a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

OR

Using Gauss' law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point

(i) outside and (ii) inside the shell.

Plot a graph showing variation of electric field as a function of r > R and r < R. (r being the distance from the centre of the shell)

[2014]Q.1 Two equal balls having equal positive charge ‘q’ coulombs are suspended by two insulating strings of

equal length. What would be the effect on the force when a plastic sheet is inserted between the two?

Q.2 A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

Q.3 Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere’s circuital law to include the term due to displacement current.

Q.4 Draw a labelled diagram of Van de Graaff generator. State its working principle to show how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

OR

(a) Deduce the expression for the torque acting on a dipole moment p in the presence of a uniform electric field E.

(b) Consider two hollow concentric spheres, S1 and S2, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the spheres S1 change if a medium of dielectric constant ‘r’ is introduced in the space inside S1 in place of air? Deduce the necessary expression.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(12)

Page 13: Electrostatics 2014

SAMPLE PAPER

Q.1 Which physical quantity has its SI unit as?

(i) C – m. (ii) V m-1

Q.2 Two identical plane metallic surfaces ‘A’ and ‘B’ are kept parallel to each other in air, separated by a distance of 1cm. As shown in the figure.

A is given a positive potential of 10V and the outer surface of B is earthed.

(i) what is the magnitude and direction of the uniform electric field between ‘Y’ and ‘Z’?

(ii) what is the work done in moving a charge of 20 C from ‘X’ to ‘Y’?

Q.3 Two capacitors, of capacitance 3F and 6F, are charged to potentials of 2V and 5V respectively. These two charged capacitors are connected in series. Find the potential across each of the two capacitors now?

Q.4 Three charges -2 C, 22 C and - 2 C are arranged along a straight line as shown in the figure. Calculate the total electric field intensity due to all these three charges at the point ‘P’.

Or

A point charge of +2C is kept fixed at the origin. Another point charges of +4C is brought form a far off point to a point distant 50cm form the origin. Calculate the electrostatic potential energy of this two-charge system?

Another charge of +1C is brought to a point distant 100cm. From each of these two charges (assumed to be kept fixed). What is the work done?

Q.5 An electric dipole with moment ‘p’ is placed in a uniform electric field of intensity ‘E’. Write the expression for the torque ‘’ experienced by the dipole. Identify two pairs of perpendicular vector in the expression?Show diagrammatically the orientation of the dipole in the field for which the torque is

(i) maximum(ii) half the maximum value(iii) zero

Q.6 Obtain an expression for the energy stored in a parallel plate capacitor. In the following figure, the energy stored in C4 is 27J? Calculate the total energy stored in the system.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(13)

A B

Y

X

Z

A

1 m

P

B

1m 1 m

-2C 22C -2C

C

P

1f

C1 Q

3f

6f

C2

C3

C4

2f

R

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3

Q.7 With the help of circuit diagram, explain how would you compare the emf of two primary cells using a potentiometer?

Q.8 Two capacitors of capacitances C1 = 3 f and C2 = 6 f arranged in series are connected in parallel with a third capacitor C3 = 4 f. The arrangement is connected to a 6.0V battery. Calculate the total energy stored in the capacitors?

Q.9 Why does the electrical field inside a dielectric decrease when it is placed in an external electric field?Q.10 Calculate the equivalent capacitance between the points ‘A’ and ‘B’ in the following combination.

Q.11 A glass rod rubbed with silk is brought close to two uncharged spheres in contact with each other inducing charge on them as shown in figure. Explain with diagram in each case what happens when

(i) The spheres are slightly separated?(ii) The glass rod is subsequently removed?(iii) The spheres are separated far apart?

Q.12 Two point charges ‘q1’ and ‘q2’ are placed close to each other in air. What is the nature of the force between them when

(i) q1q2 > 0. (ii) q1q2 < 0.

Q.13 State the principle of working of Van de Graff Generator? Give its one main application?Q.14 The adjoining figure shows the variation of electrostatic potential ‘V’ with distance ‘X’ for a given

charge distribution. From the points marked ‘A’, ‘B’ & ‘C’, identify the point at which the electric field is(i) zero(ii) maximum

Explain your answer in each case?

Q.15 Two point charges q1 = 5.4 10-6 C and q2 = -5.4 10-6 C are located at the points A (0, - 5) and B (0, +5) respectively in ‘XY’ plane, the distances being measured is meters. Draw a schematic diagram and calculate the electric dipole moment of this charge system. Mark one point each in the diagram where the electric field of this charges system is (a) parallel to its dipole moment (b) anti – parallel to its dipole moment

Q.16 Write the SI unit of (i) Potential gradient, (ii) Electric dipole moment?

Q.17 A student is asked to calculate the ratio of electric flux through the surfaces of sphere ‘S1’ and ‘S2’ with charges

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A D E F GB

C1=5F C2=10F

C3 = 15 F

C4= 30 F

A B+ + ++

+

--

+ ---

+ + +

+ + +

A B

C

V

X

S1

S25cm

10 cm

+3c

+1c

Page 15: Electrostatics 2014

placed inside, as shown in the figure. He gets the answer as 4:1 check the correctness of the answer by actually calculating the electric flux ratio through the two surfaces and state whether his answer is correct or incorrect?

Q.18 Two circular metal plates each of radius 10cm, are kept parallel to each other at a distance of 1mm. What kind of capacitor do they make? Mention one application of this capacitor.

If the radius of each of the plates is increases by a factor of 2 and their distance of separation decreased to half of its initial value, calculate the ratio of the capacitance in the two cases.

Suggest any one possible method by which the capacitance in the second case be increased by n times?

Q.19 Define the term resistively? Write an expression for the resistivity of a conductor in terms of relaxation time?

Q.20 When an uncharged body ‘B’ is charged by induction, using a charged body ‘A’, the charge on ‘A’ does not change. Explain how this fact is in accordance with the principle of conservation of charge?

Q.21 State any two properties of the electric lines of force. Draw the lines of force in each of the following cases: -

(a) An isolated point charge (i) q >0 (ii) q <0.

(b) Between the plates of a charged parallel plate capacitor.Q.22 Two charges of magnitude +25nC and –9nC are located at points A (1, 2) and B (5, 2) respectively.

Find the magnitude of electric field due to these charges at the point C (5, 5). All distances are measured in meters?

Q.23 Define the term potential gradient? Using this concept, explain the method for comparison of emf of two primary cells using a potentiometer? Establish the relation used. Write two possible causes of potentiometer giving only one-sided deflection in this method?

Q.24 Is electric flux a scalar or a vector quantity? Write its SI unit. Q.25 A sphere S1 of radius r, encloses a total charge Q. If there is another concentric sphere S2 of radius r2

(r2 > r1) and there be no additional charges between S1 and S2 find the ratio of the electric flux through S1 and S2.

Q.26 A parallel plate capacitor with air between its plates having plate area of 6 10-3 m2 and separation between them 3 mm is connected to a 100 V supply. Calculate charge on each plate of the capacitor. Explain what would happen a 3 mm thick mica sheet (dielectric constant = 6) is inserted between the plates.(a) while the voltage supply remains connected.(b) after the supply is disconnected.

Q.27 Keeping the voltage of the charging source constant, what would be the percentage change in the energy stored in a parallel plate capacitor if the separation between its plates were to be decreased by 10%?

Q.28 A charge Q located at a point is in equilibrium under the combined electric field of three charges q1, q2, q3. If the charges q1, q2 are located at points and respectively, find the direction of the force on

Q, due to q3 in terms of q1, q2, , and . Q.29 What is the angle between the directions of electric field at any (i) axial point and (ii) equitorial point

due to an electric dipole? Q.30 Four point charges are placed at the four corners of a square in the two ways (i) and (ii) as shown

below. Will the(i) electric field(ii) Electric potential, at the centre of the square, be the same or different in the two configurations

and why?

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Page 16: Electrostatics 2014

Q.31 The following data was obtained for the dependence of the magnitude of electric field, with distance, from a reference point O, within the charge distribution in the shaded region.(i) Identify the charge distribution and justify your answer.(ii) If the potential due to this charge distribution, has a value

V at the point A, what is its value at the point A`? 3

Filed Point A B C A` B` C`Magnitude of electric field

E E/8 E/27 E 2 E 16 E/64

Q.32 Two indentical plane metallic surfaces A and B are kept parallel to each other in air separated by a distance of 1.0 cm as shown in the figure.

Surface A is given a positive potential of 10V and the outer surface of B is earthed. (i) What is the magnitude and direction of the uniform electric field between points Y and Z? (ii) What is the work done in moving a charge of 20 C from point X and point Y?

Q.33 An electric dipole of dipole moment is placed in a uniform electric field. Write the expression for the torque experienced by the dipole. Identify two pairs of perpendicular vectors in the expression. Show diagramatically the orientation of the dipole in the field for which the torque is (i) Maximum (ii) Half the maximumvalue (iii) Zero.

Q.34 Show that during the charging of a parallel plate capacitor, the rate of change of charge on each plate equals times the rate of change of electric flux linked with it. What is the name given to the term?

Q.35 State the theorem, which relates the enclosed charge, inside a closed surface, with the electric flux through it. Use this theorem to obtain the electric field due to a uniformly charged thin spherical shell at an

(i) outside point (ii) inside point.An electric charge of 8.85 10-13C is placed at the centre of a sphere of radius 1m. what is the total electric flux linked with the sphere? How will the electric flux change if another equal and opposite charge in introduced at a distance of

(i) 0.5m form the centre (ii) 1.5m from the centre

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-Q -Q

Q + QA B

CD-Q +Q

Q -QA B

CD

Page 17: Electrostatics 2014

Q.36 Three hollow concentric spheres ‘A’, ‘B’ and ‘C’ having radii ‘a’, ‘b’ and ‘c’ (a <b<c) have uniform surface charge densities + and + respectively. Compute the electric potential at the surface of each sphere?

Q.37 Derive an expression for the energy stored in capacitor of capacitance `C’ when if is charged by connecting it to a battery of p.d. ‘V’ Now if the capacitor is disconnected from the battery, what will be the energy stored in the capacitor. When (i) separation between plates is doubled and (ii) an uncharged and identical capacitor is connected across it.

Q.38 Two capacitors with capacity C1 and C2 re charged to potential V1 and V2 respectively and then connected in parallel. Calculate the common potential across the combination, the charge on each capacitor, the electrostatic energy stored in the system and the change in the electrostatic energy from its initial value.

Q.39 Two dipoles, made from charges q and Q, respectively, have equal dipole moments. Give the

(i) ratio between the ‘separations’ of the these two pairs of charges(i) angle between the dipole axis of these two dipoles. [1]

Q.40 N spherical droplets, each of radius r, have been charged to have a potential V each. If all these droplets were to coalesce to form a single large drop, what would be the potential of this large drop?

(It is given that the capacitance of a sphere of radius r equals 40kr)

OR

Two point charges, q1 and q2, are located at points (a, o, o) and (o, b, o) respectively. Find the electric field, due to both these charges, at the point, (o, o, c). [2]

Q.41 Find the P.E. associated with a charge ‘q’ if it were present at the point P with respect to the ‘set-up’ of two charged spheres, arranged as shown. Here O is the mid-point of the line O1, O2. [2]

Q.42 The capacitors C1, and C2, having plates of area A each, are connected in series, as shown. Campare the capacitance of this combination with the capacitor C3, again having plates of area A each, but ‘made up’ as shown in the figure. [3]

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Page 18: Electrostatics 2014

Q.43 The electric field lines in a region are shown in the figure. A and B are two points in the region. At which point a charge ‘+q’ experiences minimum force? [1]

Q.44 (a) An electron revolves around a nucleus in circular orbit. Draw the three equipotential surfaces around the nucleus.

(b) Figure below shows a cylindrical Gaussian surface ‘G’ for an infinitely long thin straight wire of uniform charge density ‘’ [3]

(i) For which surface is the electric flux zero?(ii) Over which surface is the electric field constant?

ORDefine the SI unit of capacitance. As shown in the figure given below, a dielectric material of dielectric constant 19 is inserted in half portion between the plates of a parallel-plate capacitor. If its initial capacitance is 40 μF, what will be the new capacitance?

Q.45 Mr. Kishan is a farmer who was staying happily in a hut made of hey and leafy roof. It is easy for him to renovate his home with new leaves every year as the good quality palm leaves he get free of cost and it is environment friendly. Most of the village people are satisfied with the same type of huts there.

But one day during heavy lightning, many of the huts were burnt to ashes and people were sad and disappointed. Mr. Sekhar works in electricity department and has good knowledge of current affairs. He soon reached the spot along with his friends and pacified them and made arrangements for their comfortable stay. The very next day the team could erect many lightning conductors and few cavities of metal conductors and made awareness to the villagers about lightning and the use of things installed there. (a) What according to you, are the values displayed by Mr. Sekhar and his friends to help Mr. Kishan and the village people? [2]

What is the principle behind working of a lightning conductor? Also by applying Gauss theorem show that net electric field inside the metallic cavity is zero. [2]

Q.46 Name the physical quantity whose SI unit is volt/meter. Is it a scalar or a vector quantity?

Q.47 Derive the expression for torque, acting on the dipole, placed in a uniform electric field.

CBSE TWENTY TWO YEAR PAPERS AURORA CLASSES(18)

Page 19: Electrostatics 2014

Q.48 You are given three capacitors of value 2μF, 3μF, 6μF. With suitable diagram explain how will you connect them to a resultant capacity of 4μF?

Q.49 A 200 V cell is connected to an 8 μF capacitor and removed after the capacitor is fully charged. Also, an uncharged 4 μF capacitor is connected to this 8 μF capacitor in parallel.

(a) What is the potential difference across the combination?

(b) What is the charge on each capacitor?

Q.50 A capacitor, of capacitance C, is being charged up by connecting it across ad.c. voltage source of voltage V. How do the conduction and displacement currents, in this set up compare with each other

(a) during the charging up process?

(b) after the capacitor gets fully charged?

Q.51 Two electrically charged particles, having charges of different magnitude, when placed at a distance ‘d’ from each other, experience a force of attraction ‘F’. These two particles are put in contact and again placed at the same distance from each other.

What is the nature of new force between them?

Is the magnitude of the force of interaction between them now more or less than F?

Q.52 Find the amount of work done in rotating an electric dipole, of dipole moment 3 10-8 cm, from its position of stable equilibrium, to the position of unstable equilibrium, in a uniform electric field of intensity 104 N/C.

Q.53 Find the potential difference across each cell and the rate of energy dissipation in R

Q.54 State the principle of a machine that can build up high voltages of the order of a few million volts. Also explain the construction and working of this machine.

OR

Three identical parallel plate (air) capacitors C1, C2, C3 have capacitances C each. The space between their plates is now filled with dielectrics as shown. If all the three capacitors, still have equal capacitances, obtain the relation between the dielectric constants K, K1, K2, K3 and K4.

Q.55 Charges of magnitudes 2 Q & - Q are located at points (a, 0, 0) and (4a, 0 ,0). Find the ratio of the flux of electric field due to these charges, through concentric spheres of radii 2a and 8a centered at the origin.

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Page 20: Electrostatics 2014

Q.56 Find the amount of work done in arranging the three point charges, on the vertices of an equilateral triangle, ABC of side 10 cm, as shown in the figure.

Q.57 Find the expression for the electric field intensity, and the electric potential, due to a dipole at a point on the equiatorial line. Would the electric field be necessarily zero at a point where the electric potential is zero? Give an example to illustrate your answer.

OR

Find the expression for the capacitance of a parallel plate capacitor of area A and plate separation d if (i) a dielectric slab or thickness t, and (ii) a metallic slab of thickness t, where (t?d) are introduced one by on between the plates of the capacitor. In which case would the capacitance be more and why?

OR

Explain the formation of the depletion region for a P-N Junction. How does the width of this region change when the junction is

(i) Forward biased, and (ii) reverse based.(ii) How does an increase in the doping concentration affect the width of the depletion region?

Q.58 What is the equivalent capacitance, C, of the five capacitors, connected as shown?

Q.59 Justify that the electrostatic potential is constant throughout the volume of a charged conductor and has the same value on its surface as inside it.

OR

A capacitor is charged with a battery and then the its plate separation is increased without disconnecting the battery. What will be the change in

(a) charge stored in the capacitor?(b) Energy stored in the capacitor? (c) Potential difference across the plates of the capacitor?(d) Electric field between the plates of the capacitor?

Q.60 Using Gauss law establish that the magnitude of electric intensity, at a point, due to an infinite plan sheet, with uniform charge density is independent of the distance of the field point.

OR

Define an electric field line. Draw the pattern of the field lines around a system of two equal positive charge separated by a distance.

Q.61 A charged particle, of charge 2 C and mass 10 milligram, moving with a velocity of 1000 m/s entres a uniform electric field of strength 103NC-1 directed perpendicular to its direction of motion. Find the velocity, and displacement, of the particle after 10s.

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