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Electric Potential

This lecture explains the concept of electric potential and its relation to energy between charges. It covers topics such as potential from a point charge, potential of a dipole, potential from continuous distributions, and potentials from line and disk charges.

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Electric Potential

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  1. Electric Potential PH 203 Professor Lee Carkner Lecture 7

  2. Potential U = Vq V = ∫ E ds • For a point charge (q): V = (1/4pe0)(q/r)

  3. Groups of Charges • Since energy is a scalar, potential is too • The potential at a given point is the algebraic sum of the effects of each charge that acts on the point • Where V = kq/r (for a point charge), and each charge has its own q and r

  4. Energy Between Charges U = q2V = kq1q2/r • This potential energy is relative to an infinite separation • Or separate them, if they have opposite charge

  5. Systems of Charge • Find the energy for each charged paired with every other charge • We generally solve for the external work • If the charges have opposite signs, it takes negative work to bring them together • They will do it themselves

  6. Potential from Dipole V = k[(q/r(+)) + (-q/r(-))] • If the distance between the charges is small and if the point of interest is at an angle q to the dipole moment, V = (k p cos q )/ r2 • where p = qd, the dipole moment

  7. Continuous Distribution • The potential from each is just V = k dq / r V = k ∫ dq / r • We need expressions for dq and r that we can integrate

  8. Potential from Line • The charge: dq = l dx • r = (x2 + d2)½ • Integrating from x = 0 to x = L V = (kl) ∫ (1 / (x2 + d2)½ ) V =(kl) ln [(L + (L2 + d2)½ ) / d] • where “ln” is the natural log

  9. Potential from Disk • Our charge element is a ring of radius R’ and width dR’ • Its charge is s times the ring’s area: • dq = s(2pR’)(dR’) • r = (z2 + R’2)½ V = s/2e0∫ R’dR’/((z2 + R’2)½) V = s/2e0 ((z2 + R2)½ - z)

  10. Next Time • Read 25.1-25.4 • Problems: Ch 24, P: 16, 69, 70, Ch 25, P: 4, 8 • Test #1 is next Monday • Covers Chapters 21-25 • Multiple choice and problems • Equations and constant provided • Sample equation sheet on web page

  11. If a charged particle moves along an equipotential line (assuming no other forces), • Its potential energy does not change • No work is done • Its kinetic energy does not change • Its velocity does not change • All of the above

  12. A positive particle moves with the field. What happens to the potential? : What happens to the potential energy? • Increase : Increase • Increase : Decrease • Decrease : Decrease • Decrease : Increase • Stay the same : Stay the same High Potential E + Low Potential

  13. A positive particle moves against the field. What happens to the potential? : What happens to the potential energy? • Increase : Increase • Increase : Decrease • Decrease : Decrease • Decrease : Increase • Stay the same : Stay the same High Potential E + Low Potential

  14. A negative particle moves with the field. What happens to the potential? : What happens to the potential energy? • Increase : Increase • Increase : Decrease • Decrease : Decrease • Decrease : Increase • Stay the same : Stay the same High Potential E - Low Potential

  15. A negative particle moves against the field. What happens to the potential? : What happens to the potential energy? • Increase : Increase • Increase : Decrease • Decrease : Decrease • Decrease : Increase • Stay the same : Stay the same High Potential E - Low Potential

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