Lecture 6-Lecture 6-11

Please read the textbook before each Lecture and

Come to the lecture with questions

The chapter to be covered is at the end of the syllabus

Lecture 6-Lecture 6-22Thin sheet of any charge distribution

'R diskE E E 'L diskE E E

Just to left of disk

Just to right of disk

0 0

0

( ' )

( ' )

2 2

disk

disk

disk disk

E E E

E E

E E

n

n

tiny disk

0nE

Lecture 6-Lecture 6-33 Electrostatic Shielding (Continued)

++++

+

+

Add Q’ If you now add charge Q’ to the conductor and/or Q’’ on the outside of the conductor, the interior electric fields do not change.

Q’’

If you move charge q in the cavity, the exterior electric fields and the extreior charge distribution are not affected.

Conducting shell electrostatically shields its exterior from changes on the inside.

q

Conducting shell electrostatically shields its interior from changes on the outside, too.

Lecture 6-Lecture 6-44Gravitational vs Electrostatic Potential Energy

( ) ( )b

a

U U b U a

dF l

a

bqE

mg

Gravity Coulomb

b

aldF

b

a

Lecture 6-Lecture 6-55Electric Potential Energy of a Charge (continued)

i is “the” reference point. Choice of reference point (or point of zero potential energy) is arbitrary.

0

dl

i is often chosen to be infinitely far ( )

0

( ) ( )r

i

U U r U i

q E dl

r

ildEq0

Lecture 6-Lecture 6-66Potential Energy in the Field due to a Point Charge q

0

02

02

0 0

( )P

P

r

r

U r q E dl

q qk r dl

lq qk dll

q q q qk k

l r

From ∞

This is also called the potential energy of the two-charge configuration of q and q0.

P

ldEq0

Lecture 6-Lecture 6-77Potential Energy of a Multiple-Charge Configuration

1 2 /kq q d

1 31 32 2

2q q qq qk k k

ddq

d

dqqk

dqqk

dqqk

dqqk

dqqk

dqqk

22413243423121

Lecture 6-Lecture 6-88Physics 241 –Warm-up quiz

Three point charges carry the same charge -q. Which of the following statements is true? Select one of (a) – (e).

A. An electron would have a higher potential energy at point A than at point B

B. A proton would have a higher potential energy at point A than at point B

C. An electron would have a lower potential energy at point A than at point B

D. The potential energy is the same for an electron and a proton at point A.

E. The potential energy is the same for a proton at point A and point B.

A B-q-q

-q

Lecture 6-Lecture 6-99Electric Potential

• So U(r)/q0 is independent of q0, allowing us to introduce electric potential V independent of q0.

0

( )( ) U rV rq

• U(r) of a test charge q0 in electric field generated by other source charges is proportional to q0 .

0

( )( ) U rV rq

taking the same reference point

rr

ldEqldEqrV 00)(

Lecture 6-Lecture 6-1010Potential at P due to a point charge q

0

0

( )( ) qU r

V rqqkr

From ∞

V(r) drop following the direction of electrical field.

Lecture 6-Lecture 6-1111Electron Volt

• V=U/q is measured in volts => 1 V (volt) = 1 J / 1 C

J N mV E m VC CN VEC m

19

1 1 1

1 | | 1 1.602 10 1

J C V

eV e V C V

• V depends on an arbitrary choice of the reference point.• V is independent of a test charge with which to measure it.

(electron volt)

Potential energy difference when 1 C of charge is moved between points of potential difference 1 V

Lecture 6-Lecture 6-1212Potential due to two (source) charges

1 2( )| | | |q qV x k kx x a

1 2 0q q

Lecture 6-Lecture 6-1313Potential due to Multiple Source Charges: Example

1 2 3 4

( )

/ 2

V Pq q q qk

d

Dotted line is an equipotential when

q1=12nC, q2= -24nC, q3=31nC, q4=17nC

E from V

xVEx

yVEy

z

VEz

Expressed as a vector, E is the negative gradient of V

VE

We can obtain the electric field E from the potential V by inverting the integral that computes V from E:

r

zyx

r

dzEdyEdxEldErV )()(

Lecture 6-Lecture 6-1515 Lightning

E = 3 x 106 N/C

at electrical breakdown of air

V on the order of 109 V

http://micro.magnet.fsu.edu/electromag/java/lightning/index.html

Examples (only a Preview)

Point charge Q: ( ) QV r kr

2( ) Q VE r k r r

r r

Charged disk: ( ) ??V z 2 2

0

( ) (1 )2

V zE z z zz z R

( ) QV r kr

2( ) QE r k rr

Uniformly charged sphere:

r > R

r < R2

20

1( ) 34 2

Q rV rR R

30

1( )4

QrE r rR

Charged sheet:0

( ) sgn( )2

E z z z

( ) ??V z

Charged line: ( ) ??V z 0

( )2

E r rr

Lecture 6-Lecture 6-1717Physics 241 –Quiz 4a

A spherical shell is uniformly charged with a positive charge density . Which of the following statements is (are) true? Select one of (a) – (e).

1. An electron would have a higher potential energy at point A than at point B

2. A proton would have a higher potential energy at point A than at point B

3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B

A B

a) 1 and 3 onlyb) 1 and 4 onlyc) 2 and 3 onlyd) 2 and 4 onlye) None of them

Lecture 6-Lecture 6-1818Physics 241 –Quiz 4b

A plane is uniformly charged with a positive charge density . Which of the following statements is (are) true? Select one of (a) – (e).

1. A proton would have a higher potential energy at point A than at point B

2. An electron would have a higher potential energy at point A than at point B

3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B

A B

a) 1 and 3 onlyb) 1 and 4 onlyc) 2 and 3 onlyd) 2 and 4 onlye) None of them

Lecture 6-Lecture 6-1919Physics 241 –Quiz 4c

A sphere is uniformly charged with a negative surface charge density . Which of the following statements is (are) true? Select one of (a) – (e).

1. A proton would have a higher potential energy at point A than at point B

2. An electron would have a higher potential energy at point A than at point B

3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B

A B

a) 1 and 3 onlyb) 1 and 4 onlyc) 2 and 3 onlyd) 2 and 4 onlye) None of them