-Electric Potential Energy and Electric Potential due to Point ChargesAP Physics C

Mrs. Coyle

Electric Potential Due to a Point Charge

Vabs = k Q / r

Electric Potential due to a Point Charge

The absolute potential of any position in its electric field is: Vabs = k Q / r.

When the charge Q creating the field is positive, the potential is positive; when the central charge Q is negative, the potential is negative. 

As r ∞ , the absolute potential is defined to be zero.

Potential Difference due to a Point Charge

1 1B A e

B A

V V k qr r

The electric potential is independent of the path between points A and B

It is customary to choose a reference potential of V = 0 at rA = ∞

Then the potential at some point r is

e

qV k

r

Electric Potential vs Distance from a Positive Point Charge

The red line shows the 1/r nature of the potential.

If the central point charge is negative, V is negative and the graph is a hole.

Electric Potential with Multiple Charges

The electric potential due to several point charges is the sum of the potentials due to each individual charge

This is an example of the superposition principle

The sum is the algebraic sum

V = 0 at r = ∞

ie

i i

qV k

r

Equipotential Lines

Simulation of Field with Equipotential Lineshttp://glencoe.mcgraw-hill.com/sites/0078458137/student_view0/chapter21/electric_fields_applet.html

Graphs of V and E vs r for a point charge E decreases more sharply

Problem 1

If the central charge was +10 mC, what is the potential at surface A whererA = 3 meters and at surface B where rB = 1 meter?

Ans: 3X10**7 V , 9X10**7 V

Problem 2Calculate the Potential and the Electric Field at the

midpoint.

What does this graph represent?

Ans: -Net E = 2kq/r2 towards the right

-Net V = 0

Problem

Find E and V at center of square in terms of q, r.