chapter 1 - electrostatics 1

8/10/2019 Chapter 1 - Electrostatics 1

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CHAPTER 1: ELECTROSTATICS

1.1 Coulombs Law

1. Three charges are arranged as shown in Figure above. Find the magnitude and direction of the electrostatic force

on the charge at the origin.

[Ans: 1.38 10at 77.5below the negative x-axis]

2. Three point charges are located at the corners of an equilateral triangle as in Figure above. Find the magnitude

and direction of the net electric force on the 2.00 charge.

[Ans: 0.437 at 85.3from the -axis.]


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3.

Two small metallic spheres, each of mass 0.20 , are suspended as pendulums by light strings from a

common point as shown in Figure above. The spheres are given the same electric charge, and it is found that they

come to equilibrium when each string is at an angle of 5.0 with the vertical. If each string has length

30.0 , what is the magnitude of the charge on each sphere?

[Ans: 7.2 ]

1.2 Electric Field

4. A small block of mass and charge is placed on an insulated, frictionless, inclined plane of angle as in

Figure above. An electric field is applied parallel to the incline. (a) Find an expression for the magnitude of the

electric field that enables the block to remain at rest. (b) If 5.40 , 7.00 , and 25.0, determine

the magnitude and direction of the electric field that enables the block to remain at rest on the incline.

[Ans: (a)

(b) 3.19 10/down the incline]

5. In Figure abovedetermine the point (other than infinity) at which the total electric field is zero.

[Ans: 1.8 to the left of the 2.5 charge]


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6.

Three identical charges ( 5.0 ) lie along a circle of radius 2.0 at angles of 30, 150, and 270, as

shown in Figure above. What is the resultant electric field at the center of the circle?

[Ans: zero]

7.

Three point charges are aligned along the -axis as shown in Figure above. Find the electric field at the position

2.0 , 0.

[Ans: 24 /in the positive -direction]

8. Each of the electrons in a particle beam has a kinetic energy of 1.60 10. (a) What is the magnitude of the

uniform electric field (pointing in the direction of the electrons movement) that will stop these electrons in a

distance of 10.0 ? (b) How long will it take to stop the electrons? (c) After the electrons stop, what will they

do? Explain.

[Ans: (a) 1.00 10/ (b) 3.37 10 (c) accelerate at 1.76 10 in the direction opposite that of the

electric field]

9. Two point charges are a small distance apart. (a) Sketch the electric field lines for the two if one has a charge four

times that of the other and both charges are positive. (b) Repeat for the case in which both charges are negative.

10.A small sphere of mass 0.60 hangs from a light string in an electric field of intensity 700 . In the

equilibrium position shown, the string makes an angle of 20with the vertical. What is the magnitude and sign of

the charge on the sphere?


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[Ans: 3.06 10]

1.3 Charge In A Uniform Electric Field

11.Two horizontal flat parallel metal plates,and , are separated by 6.0 . Each plate has a length of 1.0 . A

voltage of 1.0 is applied to while is earthed, as shown in Figure above. An electron travelling at aconstant speed of 2.5 10 passes through midpoint which lies on the horizontal line . Determine

the velocity of the electron at the moment when it just leaves the space in between the two plates. (Note:

1.76 10 )

[Ans: 2.76 10 , 25.1]

12.

Figure aboveshows a pair of parallel oppositely charged plates, and . A uniform electric field of magnitude

25 exists in the space in between the plates. An electron travelling at constant speed enters the field

through a slit at angle 60to the plate. After 6.0 , the electron leaves the field through slit . Determine:

(a) The speed of the electron before it enters the field.

(b)

The distance between and .(Note: 1.76 10

)

[Ans: (a) 1.52 10 (b) 4.6 10]

13.Two protons inside a helium nucleus are separated by a distance of 1.5 10. Determine the work required

to be done in order to bring two protons from infinity to the separation mentioned. (Charge of a proton 1.6

10)


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[Ans: 1.5 10]

14.

Electrons in an electron beam move at speed 1.0 10 . The electrons enter a region lying in between the

-plates of an oscilloscope, as shown in Figure above. The p.d. of 50 is applied to the pair of plates. Edge

effects can be neglected. Determine:

(a) The time taken by the electron to move through the region in between the plates.

(b) The vertical displacement of the electron beam when the electrons move out of the region

(c)

The value , the vertical displacement of the electron beam on the screen , if the distance between the edgeof the plates and the screen is 25.0 .

(Note: 1.80 10 )

[Ans: (a) 1 10 (b) 1.8 10 , 9.0 (c) 54 ]

1.4 Electric Potential

15.Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the

rectangle in Figure above. (b) Repeat if the 2.00 charge is replaced with a charge of 2.00 .

[Ans: (a) 2.67 10

(b) 2.13 10

]

16.Two point charges 5.00 and 3.00 are separated by 35.0 . (a) What is the electric

potential at a point midway between the charges? (b) What is the potential energy of the pair of charges? What is

the significance of the algebraic sign of your answer?

[Ans: (a) 103 (b) 3.85 10; positive work must be done to separate the charges.]


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17.

The three charges in Figure aboveare at the vertices of an isosceles triangle. Let 7.00 and calculate the

electric potential at the midpoint of the base.

[Ans: 11.0 ]

18.

In Rutherfords famous scattering experiments that led to the planetary model of the atom, alpha particles (having

charges of 2and masses of 6.64 10) were fired toward a gold nucleus with charge 79. An alpha

particle, initially very far from the gold nucleus, is fired at 2.00 10 directly toward the nucleus, as in

Figure above. How close does the alpha particle get to the gold nucleus before turning around? Assume the gold

nucleus remains stationary.

[Ans: 2.74 10]

19.

The Figure aboveshows a charge and another charge fixed at points A and B separated by 10.0 .

If 2 , calculate:


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(a) The electrical potential at the point P,

(b) The electrical potential at the point Q,

(c)

The work done to bring a charge of 5 from P to Q.

[Ans: (a) 0 (b) 3.43 10 (c) 1.72 ]

20.The graph above shows the variation of electrical potential with distance from a fixed point O along the

axis. Sketch a graph to show the variation of the electric field intensity with distance from O.

21. (a) What is the electric potential at a point (i) 10 , (ii) 50 from a point charge of 2 ?

(b) Find the work done to move a charge of 0.05 from a point 50 from the point charge 2 to a point

10 from the point charge.

[Ans: (a) (i) 1.8 10 (ii) 2.6 10 (b) 7.2 10]

22.Two parallel metal plates are connected to a 120 battery as shown in the Figure above.

Calculate:

(a) The electric field intensity between the plates,

(b) The force on an electron in between the plates,


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(c) The loss in electrical potential energy by an electron that moves from plate B to plate A. What happens to the

electrical potential energy that is lost?

[Ans: (a) 6000 (b) 9.6 10 (c) 1.92 10]

23.Point charges 10 and 5.0 are placed at points and respectively as shown in Figure

above. Determine:

(a)

The electric p.d. across and

(b) The work required in moving a point charge 2.0 from: (i) to , (ii) to infinity.

[Ans: (a) 0.82 (b) (i) 1.6 (ii) 12 ]

24.Refer to Figure above. Point charges 10 and 10 are placed at points and respectively

Determine the work required in moving a point charge 2.0 from to .

[Ans: 8.0 ]

chapter 1 - electrostatics 1

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