-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

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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
• 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
Electric Potential Due to a Continuous Charge Distribution

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
• 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
• 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 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 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 and b) E at a point along the central perpendicular axis of a Uniformly Charged Disk
• Assume the total charge of the rod is Q, length l and a linear charge density of λ.
• Hint:
Method 2 for Calculating V for a Continuous Charge Distribution:
• If E is known (from Gauss’s Law)
• Then use:
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,
Ex 25.8: Find V for a Uniformly Charged Sphere
• A solid sphere of radius R and total charge Q
• For r < R,
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