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-Electric Potential due to Continuous Charge Distributions - PowerPoint PPT Presentation

-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

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?

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)

Method 1 Charge Distribution

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

• The potential at point P due to dq

Method 1 Cont’d Charge Distribution

• 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.

Ex 25.5 : a) V Charge Distribution 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:

Ex 25.6: Find a)V electric field at P 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.

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

Ex25.7: Find V electric field at P 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:

Method 2 electric field at Pfor Calculating V for a Continuous Charge Distribution:

• If E is known (from Gauss’s Law)

• Then use:

Ex 25.8: Find V electric field at P 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,

Ex 25.8: Find V electric field at P for a Uniformly Charged Sphere

• A solid sphere of radius R and total charge Q

• For r < R,

Ex 25.8:V electric field at P for a Uniformly Charged Sphere, Graph

• The curve for inside the sphere is parabolic

• The curve for outside the sphereis a hyperbola