physics ii: electricity & magnetism

Physics II:Electricity & Magnetism

Physics II:Electricity & Magnetism

Sections 23.6 & 23.9Sections 23.6 & 23.9Sections 23.6 & 23.9Sections 23.6 & 23.9

Wednesday (Day 9)Wednesday (Day 9)

Warm-UpWarm-Up

Thurs, Mar 12Thurs, Mar 12 Calculate the electric potential at points A, B, and C due to Calculate the electric potential at points A, B, and C due to

the charges shown. Assume the charges shown. Assume VV=0 at =0 at rr=∞.=∞. What is the length difference betweenWhat is the length difference between

rrbb & & rraa?? rrbb & & rrcc??

What are the angles for What are the angles for NOANOA, , NOBNOB, and , and NOCNOC??

Place your homework on Place your homework on mymy desk: (If Applicable) desk: (If Applicable) Web Assign Problems (except for 23.10, 23.14, 23.15)Web Assign Problems (except for 23.10, 23.14, 23.15) For future assignments - check online at www.plutonium-239.comFor future assignments - check online at www.plutonium-239.com

Thurs, Mar 12Thurs, Mar 12 Calculate the electric potential at points A, B, and C due to Calculate the electric potential at points A, B, and C due to

the charges shown. Assume the charges shown. Assume VV=0 at =0 at rr=∞.=∞. What is the length difference betweenWhat is the length difference between

rrbb & & rraa?? rrbb & & rrcc??


Place your homework on Place your homework on mymy desk: (If Applicable) desk: (If Applicable) Web Assign Problems (except for 23.10, 23.14, 23.15)Web Assign Problems (except for 23.10, 23.14, 23.15) For future assignments - check online at www.plutonium-239.comFor future assignments - check online at www.plutonium-239.com

HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?

Application: Potential at various locations around two chargesApplication: Potential at various locations around two charges

Calculate the electric Calculate the electric potential at points A, potential at points A, B, and C due to the B, and C due to the charges shown. charges shown. Assume Assume VV=0 at =0 at rr=∞.=∞.

What is the length What is the length difference betweendifference between rrbb & & rraa?? rrbb & & rrcc??


Calculate the electric Calculate the electric potential at points A, potential at points A, B, and C due to the B, and C due to the charges shown. charges shown. Assume Assume VV=0 at =0 at rr=∞.=∞.

What is the length What is the length difference betweendifference between rrbb & & rraa?? rrbb & & rrcc??


A : 0 V B :−1.12x106V

Q1 =+50μCQ2 =−50μC

A

x

y

NP

O

NOC

26 cm

B

NOB

30 cm

rCrBrA

NOA

C

26 cm Q1 =−10μCQ2 =+10μC

40 cm


Application: Potential at various locations around two chargesApplication: Potential at various locations around two charges

Calculate the electric Calculate the electric potential at points A, B, potential at points A, B, and C due to the and C due to the charges shown. charges shown. Assume Assume VV=0 at =0 at rr=∞.=∞.

What is the difference What is the difference between the radii of between the radii of QQ22A, A, OOA, A, QQ11A?A?

QQ22B, B, OOB, B, QQ11B?B?

QQ22C, C, OOC, C, QQ11C?C?

What are the angles for What are the angles for Q1C, , Q1B, and , and Q1A ? ?

Calculate the electric Calculate the electric potential at points A, B, potential at points A, B, and C due to the and C due to the charges shown. charges shown. Assume Assume VV=0 at =0 at rr=∞.=∞.

What is the difference What is the difference between the radii of between the radii of QQ22A, A, OOA, A, QQ11A?A?

QQ22B, B, OOB, B, QQ11B?B?

QQ22C, C, OOC, C, QQ11C?C?

What are the angles for What are the angles for Q1C, , Q1B, and , and Q1A ? ?

A : 0 V B :−1.12x106VC

Q1 =+50μCQ2 =−50μC

Q1C

Q1BQ1A

O


Essential Question(s)Essential Question(s)

HOW DO WE DESCRIBE AND APPLY THE CONCEPT HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?OF ELECTRIC POTENTIAL? How do we determine the electric potential of an electric dipole?How do we determine the electric potential of an electric dipole?

HOW DO WE DESCRIBE AND APPLY THE CONCEPT HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?OF ELECTRIC POTENTIAL? How do we determine the electric potential of an electric dipole?How do we determine the electric potential of an electric dipole?


VocabularyVocabulary

Electric PotentialElectric Potential PotentialPotential Difference in PotentialDifference in Potential Potential DifferencePotential Difference VoltVolt VoltageVoltage Equipotential LinesEquipotential Lines Equipotential SurfacesEquipotential Surfaces Electric DipoleElectric Dipole

Electric PotentialElectric Potential PotentialPotential Difference in PotentialDifference in Potential Potential DifferencePotential Difference VoltVolt VoltageVoltage Equipotential LinesEquipotential Lines Equipotential SurfacesEquipotential Surfaces Electric DipoleElectric Dipole

Dipole MomentDipole Moment Electron VoltElectron Volt CaCathode Ray Tubethode Ray Tube Thermionic EmissionThermionic Emission CathodeCathode AnodeAnode Cathode RaysCathode Rays OscilloscopeOscilloscope

Dipole MomentDipole Moment Electron VoltElectron Volt CaCathode Ray Tubethode Ray Tube Thermionic EmissionThermionic Emission CathodeCathode AnodeAnode Cathode RaysCathode Rays OscilloscopeOscilloscope


AgendaAgenda

Electric Dipoles Electric Dipoles Derivation #1: Approximation MethodDerivation #1: Approximation Method Derivation #2: Exact Method using the Law of CosinesDerivation #2: Exact Method using the Law of Cosines Determine the Percent Difference for the Approximation Method Determine the Percent Difference for the Approximation Method

(Excel Spreadsheet)(Excel Spreadsheet) Electron VoltElectron Volt Applications of PotentialApplications of Potential Complete the following Complete the following

Lab #5: PotentialLab #5: Potential Web Assign Problems 23.10, 23.14, & 23.15Web Assign Problems 23.10, 23.14, & 23.15

Electric Dipoles Electric Dipoles Derivation #1: Approximation MethodDerivation #1: Approximation Method Derivation #2: Exact Method using the Law of CosinesDerivation #2: Exact Method using the Law of Cosines Determine the Percent Difference for the Approximation Method Determine the Percent Difference for the Approximation Method

(Excel Spreadsheet)(Excel Spreadsheet) Electron VoltElectron Volt Applications of PotentialApplications of Potential Complete the following Complete the following

Lab #5: PotentialLab #5: Potential Web Assign Problems 23.10, 23.14, & 23.15Web Assign Problems 23.10, 23.14, & 23.15


Electric DipolesElectric Dipoles

• Electric Dipoles: The combination of two equal charges of opposite Electric Dipoles: The combination of two equal charges of opposite sign, +sign, +QQ and - and -QQ, separated by a distance , separated by a distance ll. .

• The dipole moment, The dipole moment, pp: The quantity : The quantity • p=p=QlQl where Q is always defined as positive, where Q is always defined as positive, qq++. . • qq--= = p / lp / l cos cos= = p / lp / l cos(180º) = – cos(180º) = –p p / / l l • The dipole moment points from the negative to the positive charge. The dipole moment points from the negative to the positive charge. • Many molecules have a dipole moment and are referred to as polar Many molecules have a dipole moment and are referred to as polar

molecules. molecules. • It is interesting to note that the value of the separated charges It is interesting to note that the value of the separated charges maymay be less be less

than that of a single electron or proton, than that of a single electron or proton, butbut they cannot be isolated. they cannot be isolated.

• Electric Dipoles: The combination of two equal charges of opposite Electric Dipoles: The combination of two equal charges of opposite sign, +sign, +QQ and - and -QQ, separated by a distance , separated by a distance ll. .

• The dipole moment, The dipole moment, pp: The quantity : The quantity • p=p=QlQl where Q is always defined as positive, where Q is always defined as positive, qq++. . • qq--= = p / lp / l cos cos= = p / lp / l cos(180º) = – cos(180º) = –p p / / l l • The dipole moment points from the negative to the positive charge. The dipole moment points from the negative to the positive charge. • Many molecules have a dipole moment and are referred to as polar Many molecules have a dipole moment and are referred to as polar

molecules. molecules. • It is interesting to note that the value of the separated charges It is interesting to note that the value of the separated charges maymay be less be less

than that of a single electron or proton, than that of a single electron or proton, butbut they cannot be isolated. they cannot be isolated.


The potential due to an electric dipole is just the sum of the potentials due to each charge, and can be calculated exactly. However, this requires the use the law of cosines and is a very large equation for a single dipole.

By using an approximation method, a simplistic equation can be derived to calculate the potential at distances much greater than the length of the dipole moment.


Potential due to an Electric DipolePotential due to an Electric Dipole

*Approximation for determining potential far from dipole:

HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?

*Refer to the “Electric Potential due to an Electric Dipole” handout for full details regarding its derivation.

Vdipole ≈1

4πε0

pcosr2



r

L/2L/2

rr

pq

q

DUsing the Law of Cosines (Appendix A-3), r+ and r- can be determined from and :


r+2 = L

2( )2+ r

2 −2 L2( )r cos+

⇒ r+ = L2( )

2

+ rδ2 − L rδ cosθ+

r−2 = L

2( )2+ r

2 −2 L2( )r cos−

− =180° −θ+

r− = L2( )

2+ r

2 −L r cos 180°−+( )

cos 180°−+( ) =−cos+

r− = L2( )

2+ r

2 + L r cos +( )

r

L/2L/2

rr

pq

q

DTo determine V at point D:

VD =V+ +V− =1

4πε0

q+

r++

q−

r−

⎛

⎝⎜⎞

⎠⎟

VD =q

4πε0

1

L2( )

2+ r

2 −L r cos+

−1

L2( )

2+ r

2 + L r cos +( )

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

By substituting in r+ and r- into the equation above, we get



Electric DipolesElectric Dipoles

Use Excel to compare the percent Use Excel to compare the percent difference between the accurate method difference between the accurate method and approximate methodand approximate method

Use Excel to compare the percent Use Excel to compare the percent difference between the accurate method difference between the accurate method and approximate methodand approximate method

Percent Difference =actual −approximate

actualx100%


Application of Electric Dipole PotentialsApplication of Electric Dipole Potentials The dipole moment, considered as a vector, point

from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate(a) the effective charge q on the O atom. (b) the effective charge q on each H. (c) the potential 9.0 x 10-10 m from the dipole along

its axis, with oxygen being the nearer atom ( = 180º).

(d) What would the potential be at this point if only the oxygen (O) were charged?

The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate(a) the effective charge q on the O atom. (b) the effective charge q on each H. (c) the potential 9.0 x 10-10 m from the dipole along


(d) What would the potential be at this point if only the oxygen (O) were charged?

104.5º


Application of Electric Dipole Potentials (Part A)Application of Electric Dipole Potentials (Part A) The dipole moment, considered as a vector, point

from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate (a) the effective charge q on the O atom.

The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate (a) the effective charge q on the O atom.

104.5º

p=QL; L =LOH cosφBecauseoxygenisintheoppositedirectionofp,wemustusepcos ,where=180°torepresentthenegativeendofthedipole

QO =pL

=pcos

LOH cosφ=

6.1x10-30 C⋅m( )cos 180°( )

9.57x10-11m( ) cos 104.5° 2( )( )=−1.04x10-19 C

Although this charge is less than e, the smallest known charge, it is not a charge that can be isolated, but is the effective charge that results from unequal sharing of the electrons.


Application of Electric Dipole Potentials (Part B)Application of Electric Dipole Potentials (Part B) The dipole moment, considered as a vector, point

from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate(b) the effective charge q on each H.

The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate(b) the effective charge q on each H.

104.5ºp1 cosφ

p2 cosφ

Because p1 = p2 , from the vector addition we have

p = 2 p1

QH LOH

{ cos(φ) =2 QH LOH( )cos(φ);

⇒ QH =p

2Lcos(φ)=

6.1×10–30 C·m2(9.57×10–11 m)cos(104.5° 2)

QH =5.2×10–20 C


Application of Electric Dipole Potentials (Part C - Approx.)Application of Electric Dipole Potentials (Part C - Approx.) The dipole moment, considered as a vector, point

from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate(c) the potential 9.0 x 10-10 m from the dipole along


The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. Calculate(c) the potential 9.0 x 10-10 m from the dipole along


104.5º

VO =1

4πεo

pcosr2 =

14π 8.85x10−12 N ⋅m2 C2( )

6.1x1030 C⋅m( )cos 180o( )

9.0x1010 m( )2 =−0.0677V


Application of Electric Dipole Potentials (Part C - Exact)Application of Electric Dipole Potentials (Part C - Exact) The dipole moment, considered as a vector, point





104.5º

VD =q

4πε0

1

L2( )

2+ r

2 −L r cos+

−1

L2( )

2+ r

2 + L r cos +( )

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟


Application of Electric Dipole Potentials (Part C - Exact)Application of Electric Dipole Potentials (Part C - Exact)

104.5º

VO =1.04x10-20 C

4π 8.85x10−12 N⋅m2 C2( )

1

5.86x10-11m2

⎛⎝⎜

⎞⎠⎟

2

+ 9.0x10-10 m( )2− 5.86x10-11m( ) 9.0x10-10 m( ) cos 180o( )

−1

5.86x10-11m2

⎛⎝⎜

⎞⎠⎟

2

+ 9.0x10-10 m( )2+ 5.86x10-11m( ) 9.0x10-10 m( ) cos 180o( )

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟

VO =−0.0678V

VD =Q

4πε0

1

L2( )

2+ r

2 −L r cos φ+( )−

1

L2( )

2+ r

2 + L r cos φ+( )

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

p=QL

p=6.1x1030 C⋅m;

L =LOH cosφ = 9.57x1011m( ) cos 104.5° 2( )( ) =5.86x1011m

=180°Qisdefinedasthepartialpositivecharge

Q =QO =−1.04x1019 C =1.04x1019 C


Application of Electric Dipole Potentials (Part C - Exact)Application of Electric Dipole Potentials (Part C - Exact) The dipole moment, considered as a vector, point





104.5º

Percent Difference =−0.0678( )− −0.0677( )

−0.0678( )x100% =0.11%


Application of Electric Dipole Potentials (Part D)Application of Electric Dipole Potentials (Part D) The dipole moment, considered as a vector, point

from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. (d) What would the potential be at this point if only

the oxygen (O) were charged?

The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x 10-11 m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x 10-30 C•m. (d) What would the potential be at this point if only

the oxygen (O) were charged?

104.5º

If we assume that the oxygen has charge Q = -1.04 x 10-19 C, as in part a above, and that the carbon is not charged, we use the formula for a single charge:

Of course, we expect the potential of a single charge to have a greater magnitude than that of a dipole of equal charge at the same distance.

V =

14πεo

Qr

=1

4π 8.85x10−12 N ⋅m2 C2( )

−1.04x1019 C( )9.0x1010 m( )

=−1.04V > −0.0678V


Application of Electric Dipole PotentialsApplication of Electric Dipole Potentials The carbonyl group (C=O) dipole. The

distance between the carbon (+) and oxygen (-) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x 10-10 m from the dipole along its axis, with oxygen being the nearer atom ( = 180º). (c) What would the potential be at this point if only the oxygen (O) were charged?

The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen (-) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x 10-10 m from the dipole along its axis, with oxygen being the nearer atom ( = 180º). (c) What would the potential be at this point if only the oxygen (O) were charged?


Essential Question(s)Essential Question(s)

HOW DO WE DESCRIBE AND APPLY THE CONCEPT HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?OF ELECTRIC POTENTIAL? How do we apply electric potential to various applications?How do we apply electric potential to various applications?

HOW DO WE DESCRIBE AND APPLY THE CONCEPT HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?OF ELECTRIC POTENTIAL? How do we apply electric potential to various applications?How do we apply electric potential to various applications?

HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?

• One electron volt (eV) is the energy an electron gains when it is accelerated though a potential difference of one volt.

• Electron volts are useful in atomic, nuclear, and particle physics.

The Electron Volt, a Unit of Energy


Cathode Ray Tube: TV and Computer Monitors, Oscilloscope

A cathode ray tube contains a wire cathode that, when heated, emits electrons. A voltage source causes the electrons to travel to the anode.



The electrons can be steered using electric or magnetic fields.



Televisions and computer monitors (except for LCD and plasma models) have a largecathode ray tube as their display. Variations in the field steer the electrons on their way to the screen.



An oscilloscope displays en electrical signal on a screen, using it to deflect the beam vertically while it sweeps horizontally.


Electric Potentials in Technology

• Van de Graaff Accelerator

• Produces highly energetic charged particles


Electric Potentials in Technology• Field-Ion Microscope

• Images of individual atoms



• Xerography

• Relatively cheap way to make copies of anything that will fit on the glass



• Scanning Tunneling Microscope

• Can image individual atoms

• Can also move single atoms to make desired configuration


SummarySummary

The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen ( -) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x 10-10 m from the dipole along its axis, with oxygen being the nearer atom ( = 180º). (c) What would the potential be at this point if only the oxygen (O) were charged?

HW (Place in your agenda): HW (Place in your agenda): Web Assign 23.? - 23.?Web Assign 23.? - 23.?

Future assignments:Future assignments: Lab #5: Potential Lab Report (Due in 5 classes)Lab #5: Potential Lab Report (Due in 5 classes)

The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen ( -) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x 10-10 m from the dipole along its axis, with oxygen being the nearer atom ( = 180º). (c) What would the potential be at this point if only the oxygen (O) were charged?

HW (Place in your agenda): HW (Place in your agenda): Web Assign 23.? - 23.?Web Assign 23.? - 23.?

Future assignments:Future assignments: Lab #5: Potential Lab Report (Due in 5 classes)Lab #5: Potential Lab Report (Due in 5 classes)


The Electrocardiogram (ECG or EKG)

The electrocardiogram detects heart defects by measuring changes in potential on the surface of the heart.


physics ii: electricity & magnetism

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concept of electric

single dipole

dipole moment points

separated charges

quantity p

length difference betweenrb

percent difference

approximation methodderivation