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-Electric Potential due to Continuous Charge Distributions

-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

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-Electric Potential due to Continuous Charge Distributions

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  1. -Electric Potential due to Continuous Charge Distributions AP Physics C Mrs. Coyle

  2. Electric Potential –What we used so far! • Electric Potential • Potential Difference • Potential for a point charge • Potential for multiple point charges

  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

  4. Electric Potential Due to a Continuous Charge Distribution How would you calculate the V at point P?

  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)

  6. Method 1 • Consider an infinitesimal charge element dq and treat it as a point charge • The potential at point P due to dq

  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.

  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:

  9. Ex 25.5: b) Find the expression for the magnitude of the electric field at P • Start with and

  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.

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

  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:

  13. Method 2 for Calculating V for a Continuous Charge Distribution: • If E is known (from Gauss’s Law) • Then use:

  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,

  15. Ex 25.8: Find V for a Uniformly Charged Sphere • A solid sphere of radius R and total charge Q • For r < R,

  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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