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-Electric Potential due to Continuous Charge Distributions

AP Physics C

Mrs. Coyle

- Electric Potential
- Potential Difference
- Potential for a point charge
- Potential for multiple point charges

- V is a scalar quantity
- Keep the signs of the charges in the equations, so V is positive for positive charges.
- You need a reference V because it is changes in electric potential that are significant. When dealing with point charges and charge distributions the reference is V=0 when r

How would you calculate the V at point P?

- It can be calculated in two ways:
- Method 1: Divide the surface into infinitesimal elements dq
- Method 2:If E is known (from Gauss’s Law)

- Consider an infinitesimal charge element dq and treat it as a point charge
- The potential at point P due to dq

- For the total potential, integrate to include the contributions from all the dq elements
- Note: reference of V = 0 is when P is an infinite distance from the charge distribution.

Assume that the total

charge of the ring is Q.

Show that:

- Start with
and

- Assume radius a and surface charge density of σ. Assume that a disk is a series of many rings with width dr.

- Assume the total charge of the rod is Q, length l and a linear charge density of λ.
- Hint:

- If E is known (from Gauss’s Law)
- Then use:

- Assume a solid insulating sphere of radius R and total charge Q
- For r > R,

- A solid sphere of radius R and total charge Q
- For r < R,

- The curve for inside the sphere is parabolic
- The curve for outside the sphereis a hyperbola