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Continuous Charge Distributions

Continuous Charge Distributions. Electric Potential. Potential for Line of Charge. The potential of a line of charge can be found by superposing the point charge potentials of infinitesimal charge elements. so: over entire charge distribution Express all variables in terms of x

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Continuous Charge Distributions

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  1. Continuous Charge Distributions Electric Potential

  2. Potential for Line of Charge • The potential of a line of charge can be found by superposing the point charge potentials of infinitesimal charge elements.so: over entire charge distribution • Express all variables in terms of x • dx = infinitesimal length containing dq of charge

  3. Potential for Line of Charge • dq = ldx and

  4. Potential for Line of Charge • If point is perpendicular to end of line of charge, a = 0 and b = L, the length of the line and equation becomes:

  5. Potential for Line of Charge • If point is at midpoint of line, a = b = L/2 and equation is

  6. Potential for Ring of Charge

  7. Potential for Ring of Charge • The potential of a ring of charge can be found by superposing the point charge potentials of infinitesimal charge elements. • Since the potential is a scalar quantity, and since each element of the ring is the same distance r from the point P, the potential is simply given by: Q = total charge l = linear charge density

  8. Potential for Disc of Charge • The potential of a disc of charge can be found by superposing the point charge potentials of infinitesimal charge elements. • The evaluation of the potential can be facilitated by summing the potentials of charged rings

  9. Potential for Disc of Charge

  10. Potential for Disc of Charge • Write potential dV at point P: • Integrate from a = 0 to a = R

  11. Potential for Disc of Charge • The integral is of the form ∫undu, with u = x2 + a2and n = -½ • The integral evaluates to:

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