Physics 1161 Lecture 4Potential & Potential Energy

Recall Work from Phy 1151 • Work done by the force given by:

W = F d cos(θ)Positive: Force is in direction movedNegative: Force is opposite direction movedZero: Force is perpendicular to direction moved

• Careful! Ask WHAT is doing work!Opposite sign for work done by you!

• Conservative Forces Δ Potential Energy = -Wconservative

In what direction does the force on a negative charge at point A point?1) left2) right3) up

Electric field points in the direction a POSITIVE charge would feel force.

F

CheckpointUniform Electric Field 1

A B

C

Uniform E

When a negative charge is moved from A to C the ELECTRIC force does1) positive work.2) zero work.3) negative work.

-F -F -F -F -F

The work is zero because the path is perpendicular to the field

motionCheckpoint

Uniform Electric Field 2

A B

C

Uniform E

When a negative charge is moved from A to B the ELECTRIC force does

1) positive work.2) zero work.3) negative work.

-F

-F

-F

-F

-F

motion

The work is negative the electric force opposes the direction of motion

-

CheckpointUniform Electric Field 3

A B

C

Uniform E- - - - -

When a negative charge is moved from A to B, the electric potential energy of the charge

1) Increases

2) is constant

3) decreases

UE = -WE field

Like “climbing up hill” – increases potential energy

CheckpointUniform Electric Field 5

When a negative charge is moved from A to B, the electric potential energy of the charge

1 2 3

64%

29%

7%

AB

+ C1. increases2. is constant3. decreases

When a negative charge is moved from A to B, the electric potential energy of the charge

1 2 3

86%

14%

0%

AB

+ C1. increases2. is constant3. decreases

AB

+

Electric Potential Energy

- - - - -

When a negative charge is moved from A to B, the electric potential energy of the charge

(1) increases

(2) is constant

(3) decreases

1) The electric force is directed to bring the electron closer to the proton. 2) Since the electron ends up further from the proton the electric field did negative work. 3) So the electric potential energy increased

E CAC: W=0

CB: W<0

Work and D Potential Energy

• Brick raised yi yf • Charge moved ∞ rf

• FE = kq1q2/r2 (left)

• WE = -kq1q2/rf

• UE= +kq1q2/rf

W = F d cos(q)Gravity Electric

yi

yf

h

• FG = mg (down)• WG = -mgh• UG= +mgh

rf

The electric potential energy of this set of charges is:

(1) positive(2) zero(3) negative

+

+

-5 m

5 m5 m

Bring in (1): zeroBring in (2): positive Bring in (3): negative x 2

1

32

CheckpointCharges 1

Electric Potential (like height)*

• Units Joules/Coulomb VoltsBatteriesOutlets EKG

• Really Potential differences• Equipotential lines at same height • Field lines point down hill• V = k q/r (distance r from charge q)

V(∞) = 0

The electric potential at point A is _______ at point B

1) greater than

2) equal to

3) less than

To go from B to A, a positive charge must climb “up hill” – increases potential energy. Hence A is at higher potential than B

CheckpointUniform Electric Field 7

The electric potential at point A is _______ at point B

1) greater than

2) equal to

3) less than The electric field is zero at any point within a conducting material

conductor

CheckpointUniform Electric Field Conductor 1

The electric potential at A is _______ the electric potential at B.

1 2 3

63%

37%

0%

1. greater than2. equal to3. less than

+

AB

C+

The electric potential at A is _______ the electric potential at B.

1 2 3

85%

15%

0%

1. greater than2. equal to3. less than

+

AB

C+ E

1) Electric field lines point “down hill” 2) AC is equipotential path (perpendicular to E)3) CB is down hill, so B is at a lower potential than (“down hill from”) A

Electric Potential due to Proton

What is the electric potential a distance r = 0.5310-10 m from a proton? (Let V() = 0)

+

rf = 0.510-10 m

What is the electric potential energy of an electron a distance r = 0.5310-10 m from a proton?

-

kqVr

2

29 19

10

9 10 1.6 10

0.53 10

N mC

C

m

27.2 N m

C

27.2 27.2J VC

U qV 191.6 10 27.2C V 184.35 10 C V 184.35 10 JCC

Comparison:Electric Potential Energy vs. Electric Potential

• Electric Potential Energy (U) - the energy of a charge at some location.

• Electric Potential (V) - found for a location only – tells what the EPE would be if a charge were located there (usually talk about potential differences between two locations):

U = qV• Neither has direction, just location. Sign

matters!

Two Charges

Q=-3.5 μ CQ=+7.0μC

A

6 m

4 m

How much work do you have to do to bring a 2 μ C charge from far away to point A? W=ΔU= ΔVq = 1.26 x 10-2 V

• Calculate electric potential at point A due to charges– Calculate V from +7mC charge– Calculate V from –3.5mC charge– Add (EASY!)

• V = kq/rV7 = 1.26 x 104 VV3 = -0.63 x 104 V

Vtotal = 0.63 x 104 V

In the region II (between the two charges) the electric potential is

1 2 3

48%

33%

19%

Q=-3.5 mCQ=+7.0mC

I II III

1. always positive2. Positive at some points, negative at others3. Always negative

In the region II (between the two charges) the electric potential is

1 2 3

9%

59%

32%Q=-3.5 mCQ=+7.0mC

I II III

1. always positive2. Positive at some points, negative at others3. Always negative

Very close to positive charge potential is positiveVery close to negative charge potential is negative