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1. -Electric Potential due to Continuous Charge Distributions AP Physics C
2. Electric Potential ?What we used so far! Electric Potential
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
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.
9. Ex 25.5: b) Find the expression for the magnitude of the electric field at P Start with
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 s. 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 ?.
13. Method 2 for Calculating V for a Continuous Charge Distribution: If E is known (from Gauss?s Law)
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 sphere is a hyperbola