Electric Potential

another useful concept

Electrical work

• A field does work when it moves a charge.

x

Work done by field= qEx along a uniform field

Electrical work

• Charge has different potential energy U at different locations

• Potential energy is proportional to charge

–U = Work done by field = qEx

x

Electric Potential

• Potential energy per unit charge = U/q

• Depends on position

• Scalar quantity

• Unit = J/C = V = volt

Electric Potential

What is the work required to move a charged object through a field?

Work = qE·x = (U) = q = electric potential = U/unit charge

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Electric Field and Potential

Potential and Field

• Equipotential surfaces are always perpendicular to electric field lines/vectors. Why?

• Potential changes rapidly where field is strong. Why?

It makes sense from the relationships between• Electric field and electric force• Electric potential and electric potential energy• Work and potential energy• Force and work

Group Work

1. Draw field lines and equipotential surfaces around a pair of opposite charges.

2. Draw field lines and equipotential surfaces around a pair of equal charges.

Electric Potential

• U = Ufinal – Uinitial

• = final – initial

Potential is path-independent

• from a to b is the same for all paths

a

b

Question

An infinite, uniformly positively-charged plane produces a uniform electric field. How does the electric potential change with increasing distance from the plane?

A. Potential increases.

B. Potential decreases.

C. Potential is constant.

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Potential around a point charge

• Convention: = 0 at d=

• So, (r) = work/charge to bring charge from to d

• Result: W = kq1q2

d

q1

d q2

; = kq1

d

Potential of Conductors

At electrostatic equilibrium:

•Field is zero inside conductor

•potential is constant

Zero net force on all charges

Lightning Safety

This is why a car is a good place to be in a thunderstorm.

•No electric field inside

•No reason for charges to move through you

The Electron Volt eV

• Unit of energy

• eV = (Elementary charge e) · 1 volt

• Compare to Joule = (1 C)(1 V)

• e = 1.60210–19 C, so eV = 1.60210–19 J

Question

An infinite, uniformly positively-charged plane produces a uniform electric field. If the potential is V(d) a distance d from the plate, what is the potential at infinite distance?

A. Potential is +.

B. Potential is zero.

C. Potential is –.

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d

V(d)