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-Electric Potential due to Continuous Charge Distributions






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-Electric Potential due to Continuous Charge Distributions. AP Physics C Mrs. Coyle. Electric Potential –What we used so far!. Electric Potential Potential Difference Potential for a point charge Potential for multiple point charges. Remember:. V is a scalar quantity
-Electric Potential due to Continuous Charge Distributions

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Slide 1

-Electric Potential due to Continuous Charge Distributions

AP Physics C

Mrs. Coyle

Slide 2

Electric Potential –What we used so far!

  • Electric Potential

  • Potential Difference

  • Potential for a point charge

  • Potential for multiple point charges

Slide 3

Remember:

  • 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

Slide 4

Electric Potential Due to a Continuous Charge Distribution

How would you calculate the V at point P?

Slide 5

Two Ways to Calculate Electric Potential Due to a Continuous Charge Distribution

  • 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)

Slide 6

Method 1

  • Consider an infinitesimal charge element dq and treat it as a point charge

  • The potential at point P due to dq

Slide 7

Method 1 Cont’d

  • 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.

Slide 8

Ex 25.5 : a) V at a point on the perpendicular central axis of a Uniformly Charged Ring

Assume that the total

charge of the ring is Q.

Show that:

Slide 9

Ex 25.5: b) Find the expression for the magnitude of the electric field at P

  • Start with

    and

Slide 10

Ex 25.6: Find a)V and b) E at a point along the central perpendicular axis of a Uniformly Charged Disk

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

Slide 11

Ex 25.6: Find a)V and b) E at a point along the central perpendicular axis of a Uniformly Charged Disk

Slide 12

Ex25.7: Find V at a point P a distance a from a Finite Line of Charge

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

  • Hint:

Slide 13

Method 2 for Calculating V for a Continuous Charge Distribution:

  • If E is known (from Gauss’s Law)

  • Then use:

Slide 14

Ex 25.8: Find V for a Uniformly Charged Sphere (Hint: Use Gauss’s Law to find E)

  • Assume a solid insulating sphere of radius R and total charge Q

  • For r > R,

Slide 15

Ex 25.8: Find V for a Uniformly Charged Sphere

  • A solid sphere of radius R and total charge Q

  • For r < R,

Slide 16

Ex 25.8:V for a Uniformly Charged Sphere, Graph

  • The curve for inside the sphere is parabolic

  • The curve for outside the sphereis a hyperbola


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