Electric PotentialElectric Potential

Electric Potential: UVq

or U qV

Units: 1 volt V = 1 joule/coulomb•V is a SCALAR •V is determined to within an arbitrary constant. •We can choose to set V=0 at any position (most often at “r=infinity”)•There is no absolute potential

Note: electric potential V is not the same as electric potential energy U !!

Rule: Electrostatic field lines always point to decreasing electric potential. Why?

chargeenergy potential

V

What does a potential difference of 1 volt mean?1 Volt= 1J/C

It means one joule of work needs to be done to move one coulomb of charge through a potential difference of one volt.

This work could be negative or positive dependingon the sign of the charge and whether the field or us does the work and whether the charge moves from a higher to a lower potential or vice-versa.

Electric PotentialElectric Potential(not the same as electric potential energy)

“Test charge” +q moves A small displacement ds

+ EqF

Find: element of work dW done by the field.

ds

E

A

B

q

Recall…

dsEdsF qdW

fielddW dU

The work is proportional to the charge. The electric force is conservative, so we can define an electrostatic potential energy U for the charge in the electric field such that:

We then define electric potential difference dV bydU qdV so that dV = - E •ds

Note: dV does not depend on the charge q. It onlydepends on the field and a displacement in the field.

When the field does work on the test charge, electrostatic potential energy is converted to other forms of energy, such as kinetic.

Eg: a charge q of mass m starts from rest in a field E. What will its kinetic energy be after it moved a distance d in the field ?

W=Fd=qEd

W=∆K= ½ m∆v2

Eg: Point a is at 5V and point b is at 10V. The charge moved is +3C.

a) How much work is done by the field moving the charge from a to b?

b) How much work is done by the field moving the charge from b to a?

c) How much work is done by us moving the charge from a to b?

d) How much work is done by us moving the charge from b to a?

:

field

us

recall W UW U

ExamplExample: e:

Find to accelerate electrons to 107 m/s. V191.60 10e x C and kgxme

3110119 .

V1

- -

V2

01 v smxv 72 101

““Electron VoltElectron Volt” (eV):” (eV):• A unit of energy. Recall U=qV

J19-1.6x10eV 1

1 joule = 1 coul-volt and 1 C = 6.2x1019 e, so

1 J= 6.2x1019 eV. Therefore

The unit eV is useful for energy levels in an atom

““EQUIPOTENTIALS”EQUIPOTENTIALS”

• Are surfaces on which V = constant

• Are always perpendicular to the electric field

• A conductor is always an equipotential (if no current inside it)

• Closely spaced equipotential surfaces implies large E

• Widely spaced equipotential surfaces implies weak E

Uniform Electric Field:Uniform Electric Field:

+ F

a

bsq E

HigherPotential V

LowerPotential V

Work we do is:( ( ) ( ))

usW U q Vq V b V a

b

Quiz: A conductor with charges in static equilibrium on it has constant potential on its surface and interior.Recall, E=0 inside. So the surface of the conductor is an equipotential surface.

V=5VInside too

V=5V

V=5V

V=5V

What is the sign of charge, if any, on the surface of the conductor?

A) positive B) negative C) zero D) need more info !

New unit for electric field:

So unit for E is V/m which we can use instead of N/C.

Finding E given electric potential:

In one dimension, given V(x), using the result above we get:

x

dVEdx

For example, find E at x=2m whenV(x)=2+3x-x2 volts

Recall that dV = - E •ds

Example:Example:

+

-2 mm

a) Find electric field strength between platesb) Sketch a few equipotential surfaces

20V

Summary: Electric PotentialSummary: Electric Potential

chargeenergy potential

V

U qVx

dVEdx

field

usW U q VW U q V