lecture 6-1 thin sheet of any charge distribution just to left of disk just to right of disk tiny...

Lecture 6-Lecture 6-11

Thin 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


Charges and fields of a conductor

• In electrostatic equilibrium, charges inside a conductor do not move. Thus, E = 0 everywhere in the interior of a conductor.

• Since E = 0 inside, there are no net charges anywhere in the interior. Net charges can only be on the surface(s).

The electric field must be perpendicular to the surface just outside a conductor, since, otherwise, there would be currents flowing along the surface.

0

Lecture 6-Lecture 6-33Electrostatic 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.


READING QUIZ 1

IN WHAT DIRECTION CAN YOU MOVE A TEST CHARGE RELATIVE TO AN ELECTRIC FIELD SO THAT THE ELECTRIC POTENTIAL DOES NOT CHANGE?

A| Move in the direction of the electric field lines.

B| Move opposite to the direction of the electric field lines.

C| Move from point A in the electric field to point B in

in the electric field along an arbitrary path.

D| Move relative to the electric field along a path which is

everywhere perpendicular to the electric field.


Electric Potential Energy of a Charge in Electric Field

• Coulomb force is conservative => Work done by the Coulomb force is path independent.

• Can associate potential energy to charge q0 at any point r in space. ( )U r

It’s energy! A scalar measured in J (Joules)

d l

ldEqdW 0

ldEqdWdU 0

Lecture 6-Lecture 6-66Electric Potential Energy of a Charge (continued)

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

0

d l

i is often chosen to be infinitely far ( )

ldEqdW 0

ldEqdWdU 0

0

( ) ( )r

i

U U r U i

q E dl

��

r

ildEq0


Gravitational vs Electrostatic Potential Energy

( ) ( )b

a

U U b U a

dF l

a

b

qE��

mg��

Gravity Coulomb

mg l qE l

Work done by gravity or the Coulomb force decreases the potential energy.

(if g, E uniform)

b

aldF

Lecture 6-Lecture 6-88Potential 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

l

q qk dl

l

q q q qk k

l r

��

From ∞

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

What is the work required to bring q0 in from infinity?

P

ldEq0

Lecture 6-Lecture 6-99Potential Energy of a Multiple-Charge Configuration

(a)

(b)

(c)

1 2 /kq q d

1 31 32 2

2

q q qq qk k k

dd

q

d

2 3

1 3 3 41 2 2 4

1 4

2 2

q q q qq q q qk k k k

d dq q q q

k k

d

d d

d

Lecture 6-Lecture 6-1010Physics 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 6-1111Electric Potential

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

0

( )( )

U rV r

q

• [Electric potential] = [energy]/[charge] SI units: J/C = V (volts)

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

0

( )( )

U rV r

q

taking the same

reference point

Potential energy difference when 1 C of charge is moved between points of potential difference 1 V1 J

Scalar!


Potential at P due to a point charge q

0

0

( )( ) qU r

V rq

qk

r

From ∞


Electron Volt

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

J N mV E m V

C CN V

EC 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 DIFFERENCES V2 – V1


DOCCAM 2


Potential due to two (source) charges

1 2( )| | | |

q qV x k k

x x a

1 2 0q q


Potential due to Multiple Source Charges: Example

1 2 3 4

( )

/ 2

V P

q q q qk

d

Dotted line is an equipotential when

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

E from V

x

VE

x

y

VE

y

z

VE

z

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 )()(


Lightning

E = 3 x 106 N/C

at electrical breakdown of air

ΔV on the order of 109 V

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


DOCCAM 2

Examples (only a Preview)

Point charge Q: ( )Q

V r kr

2

( )Q V

E r k r rr r

��

Charged disk: ( ) ??V z 2 2

0

( ) (1 )2

V zE z z z

z z R

��

( )Q

V r kr

2( )

QE r k r

r

��

Uniformly charged sphere:

r > R

r < R2

20

1( ) 3

4 2

Q rV r

R R

30

1( )

4

QrE r r

R

��

Charged sheet:0

( ) sgn( )2

E z z z

�� ( ) ??V z

Charged line: ( ) ??V z 0

( )2

E r rr

��

Lecture 6-Lecture 6-2121Physics 241 – 10:30 Quiz 3

A spherical shell is uniformly charged with a positive charge density σ. 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

σ

Lecture 6-Lecture 6-2222Physics 241 – 11:30 Quiz 3

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

-σ

lecture 6-1 thin sheet of any charge distribution just to left of disk just to right of disk tiny...

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