Electric Potential: Concept, Conservation, and Calculation, Study notes of Electromagnetism and Electromagnetic Fields Theory

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Ch24d-Electric Potential-Revised 8/23/

Chapter 24

Electric Potential

Ch24d-Electric Potential-Revised 8/23/

Electric Potential

1. Potential Difference2. Potential Due to a System of Point Charges3. Computing the Electric Field from the Potential4. V for Continuous Charge Distributions5. Equipotential Surfaces6. Electrostatic Potential Energy

Ch24d-Electric Potential-Revised 8/23/

Gravitational Analogy The positive charge is used to make the

analogy more transparent.

Ch24d-Electric Potential-Revised 8/23/

If you throw a ball straight up in the air its initial kineticenergy is soon reduced to zero at the top of its motion.The “loss of kinetic energy” is only apparent. The kineticenergy is restored to its original value when the ball returnsto its starting position.The use of the concept of potential energy allows us tomaintain the conservation of total mechanical energy

Total Mechanical Energy = KE + PE

An Example from Last Semester

Ch24d-Electric Potential-Revised 8/23/

Work and the Conservative Force

The characteristic of a conservative force is that the workdone on an object moving it, in a force field, from point Ato point B is

independent of the path

taken between A and

B. If the path forms a closed loop then the work done is zero.

∫^

^

C

W =

F

dL = 0

Ch24d-Electric Potential-Revised 8/23/

Potential Energy - Potential Function^ There is a

potential energy

(U) and a

potential function

(V) and they are closely related.

^

i

^

^

i

dU = -F dL

F = qE dU = -qE dL

∫

^

i

^

i

^

i

(^00)

b

b^

a

a

0

dU = -q E dL

dU

dV

= -E dL

q

U

V = V - V =

E dL

q

Potential Energy

Potential Function

Ch24d-Electric Potential-Revised 8/23/

Potentials for Discrete Charges

MFMcGraw-PHY 2426

Ch24d-Electric Potential-Revised 8/23/

Potential and the Reference Point

The potentialfunction needs acommon referencepoint so that thecalculated potentialdifferences willhave physicalmeaning.

Ch24d-Electric Potential-Revised 8/23/

Potential Due to Two Point Charges Find V at points P

1 and P

2

∑

i^

1

2

i^

i^

1

2

kq

kq

kq

V =

=

r^

r^

r

1

9

1

2

P

1

2

kq

kq

kq

9x10 * 5.0x

V

=

= 2

= 2

= 2247 V

r^

r^

r^

.

2

9

-^

9

1

2

P^

'^

'

1

2

kq

kq

9x10 * 5.0x

9x10 * 5.0x

V

=

=

= 1200 V

r^

r^

.

.

MFMcGraw-PHY 2426

Ch24d-Electric Potential-Revised 8/23/

Potential Calculation for 2 Point Charges

∑

i^

1

2

i^

i^

1

2

kq

kq

kq

V =

=

r^

r^

r

1

2

kq

kq

V =

x

x - a

MFMcGraw-PHY 2426

Ch24d-Electric Potential-Revised 8/23/

Electric Dipole Geometry for Potential

Calculation

The dipole configuration requires equal and opposite charges.

(^

) 2

2

kql

l

V =

; x >

2

l

x^

-^

4

≈^



2

2

kql

kp

V

=

; x

l

x^

x p = ql is the dipole moment

MFMcGraw-PHY 2426

Ch24d-Electric Potential-Revised 8/23/

3D Image of the Electric Dipole Potential

Ch24d-Electric Potential-Revised 8/23/

Potentials for Continuous Charge

Distributions

Ch24d-Electric Potential-Revised 8/23/

Potential Due to a Ring Charge