Phys 133 – Chapter 301 Chapter 28 Electric Potential.

Phys 133 – Chapter 30 1

Chapter 28

Electric Potential

Phys 133 -- Chapter 29 2

Looking ahead

New force (Chapter 25)

New potential energy (Chapter 28)

Phys 133 -- Chapter 29 3

Electric Potential Energy (Uelec)

• Potential energy ~ Gravitational ~ Uniform electric field~ Point charge

Phys 133 -- Chapter 29 4

Gravitational potential (energy)Defined

Then defined

For the gravitational force

In general

Phys 133 -- Chapter 29 5

Uniform field: Electric potential energy

where

Phys 133 -- Chapter 29 6

s

Uniform field: Electric potential energy

s

Direction of lower potential energy depends on type of charge

Lower potential energyLower potential energy

Positive charge Negative charge

Phys 133 -- Chapter 29 7

Do Workbook 29.6

Phys 133 -- Chapter 29 8

A proton is released from rest at the positive plate of a parallel plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the speed if the experiment is repeated with double the amount of charge on the capacitor plates?

(Ans: 7.07x104 m/s)

Problem 29.3

Phys 133 -- Chapter 29 9

Electrical Potential Energy of Two Point Charges

where

Phys 133 -- Chapter 29 10

Question

b) Two point charges (+/- Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same?

a) Two point charges (both +Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same?

Phys 133 -- Chapter 29 11

Question ans

Like chargesOpposite charges

Phys 133 -- Chapter 29 12

Do Workbook 29.3

Phys 133 -- Chapter 29 13

An electron (q=-e) is sent from very far away towards a charged sphere (Q=-0.25 nC). It gets to a distance of 1.10 mm from the center of the sphere before turning around.

What is the initial speed of the electron?

(Ans: 2.68x107m/s)

What was the speed of the same electron with same initial conditions when it was 2.20 mm away?

e=1.6x10-19C, me=9.1x10-31 kg, K=9x109 Nm2/C2

Problem

Phys 133 -- Chapter 29 14

Problem ans

Phys 133 -- Chapter 29 15

Electric Potential (Velec)• Potential

~ Gravitational ~ Uniform electric field~ Point charge

Phys 133 -- Chapter 29 16

Electric Potential (Velec)

Potential only depends on source charges

Charge creates potential

define

Look at•Gravitational •Uniform electric field•Point charge

Phys 133 -- Chapter 29 17

Gravitational Potential

environmentobject

Environment only

Phys 133 -- Chapter 29 18

Electric potential capacitor

s0

(from before)

environmentobject

Environment only

Phys 133 -- Chapter 29 19

Capacitor: potential representations

Phys 133 -- Chapter 29 20

Draw V(x) for the two equipotential surfaces

Draw U(x) for a proton in these potentialsDraw U(x) for an electron in these potentials

Phys 133 -- Chapter 29 21

Workbook 29.18b extensionA proton is at x=0, moving to the right with 5x10-18 J of kinetic energy. What is its kinetic energy at point a?

What if it were an electron?

Phys 133 -- Chapter 29 22

Workbook 29.18b extension ans

proton electron

Not enough energy to reach a

Phys 133 -- Chapter 29 23

a) In the figure which capacitor plate, left or right, is the positive plate?

b) What is the electric potential energy of a proton at the midpoint of the capacitor?

c) What is the electric field strength inside the capacitor?

Problem 29.21 Modified

In general

d) What is the electric field strength inside the capacitor in terms of and o?

e) What is the electric field strength inside the capacitor in terms of ∆V and d (the distance between the plates?

Phys 133 -- Chapter 29 24

Only potential difference matters

Phys 133 -- Chapter 29 25

Electric potential two point charges

(from before)

Phys 133 -- Chapter 29 26

Point particle: potential representations

Phys 133 -- Chapter 29 27

Do Workbook 29.21

Phys 133 -- Chapter 29 28

Electric Potential: multiple charges

No vectors

Phys 133 -- Chapter 29 29

Do Workbook 29.25

Phys 133 -- Chapter 29 30

a) Find an expression for the electric potential V(x,y) for a dipole with point charges +/- Q at y= +/- a.

Problem

b) Use the result for the dipole to find the electric potential at x=2 m, y=7 m when a=2 m, and Q=2 nC.

c) What is the potential energy of a proton placed there?

Phys 133 -- Chapter 29 31

Problem ans

r+ y-a

x

x

y+ar-

Phys 133 -- Chapter 29 32

Problem plot

Phys 133 -- Chapter 29 33

Problem ans

c) What is the potential energy of a proton placed there?

b) Use the result for the dipole to find the electric potential at x=7 m, y=2 m when a=2 m, and Q=2 nC.

Phys 133 -- Chapter 29 34

Potential of continuous charge distribution

where

Then let

solve

Phys 133 -- Chapter 29 35

The figure shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.

Problem 29.69

Phys 133 -- Chapter 29 36

Problem 29.69

x

y

P (d,0)

ri

ith

xi

d

Find potential at P due to ith bit of charge

Sum up contribution from each charge at P