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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 what we used so far
Electric Potential –What we used so far!
  • Electric Potential
  • Potential Difference
  • Potential for a point charge
  • Potential for multiple point charges
remember
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
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
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
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
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
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:

slide10
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.
slide11
Ex 25.6: Find a)V and b) E at a point along the central perpendicular axis of a Uniformly Charged Disk
ex25 7 find v at a point p a distance a from a finite line of charge
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:
method 2 for calculating v for a continuous charge distribution
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
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
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
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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