Chapter 3. Electric Potential

• Constant electric field

• The Electric Potential: V

- Single Charge

- Dipole

EqF

- conservative? potential energy function?

€

rE • d

r r

r r 1

r r 2

∫ = − limq0 → 0

1

q0

[U(r r 2) −U(

r r 1)] = −[V (

r r 2) −V (

r r 1)]

ExxVConstE )(

For a point charge at the origin:

r

qrV

04

1)(

Ch3 Quiz 1

First name______________________ Last name ___________________

Section number______

There is an electric field given by

xiEE

0

where E0 is a constant. What is the difference in the value of the electric potential due to this electric field between the origin and the point x=a, y=b?

Ch3 Quiz 2

First name______________________ Last name ___________________

Section number______

There is an electric field given by

yx iyixE

22

where and are constants. What is the difference in the value of the electric potential due to this electric field between the origin and the point x=a, y=b?

Ch3 Quiz 3

There is an electric field created by some source at the origin given by

rir

cE

4

where c is a constant and r is the distance from the origin; points out from the origin. What is the difference in the value of the electric potential due to this electric field between the point x=a, y=b and the point at infinity?

ri

What is the potential function corresponding to this electric field if instead of being at the origin the source of the electric field is at point x=a, y=b?

In electrostatics:

y

UF

x

UF yx

y

VE

x

VE yx

If we know V(x,y) we can find the components of electric field and xE yE

In electrostatics, the electric field is conservative:

0rdE

1)The electric potential V in a region of space is given by

)3(),( 22 yxAyxV where A is a constant. Derive an expression for the electric field at any point in this region.

2)The electric potential V in a region of space is given by

33)(

r

crV

where c is a constant. The source of the field is at the origin. Derive an expression for the electric field at any point in this region.

Exercise 5 p. 52

An electron moves from one point to another where the second point has a larger value of the electric potential by 5 volts. If the initial velocity was zero, how fast will the electron be going at the second point?

Have a great day!

Please don’t forget your pictures

Hw: All Chapter 3 problems and exercisesReading: Chapter 3