1. Electric Potential PH 203 Professor Lee Carkner Lecture 7

2. Potential  U = Vq  V = ∫ E ds  For a point charge (q): V = (1/4  0 )(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 = q 2 V = kq 1 q 2 /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  to the dipole moment, V = (k p cos  )/ r 2  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 = dx   r = (x 2 + d 2 ) ½  Integrating from x = 0 to x = L V = (k ) ∫ (1 / (x 2 + d 2 ) ½ ) V =(k ) ln [(L + (L 2 + d 2 ) 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  times the ring’s area:  dq =  (2  R’)(dR’)   r = (z 2 + R’ 2 ) ½  V =  /2  0 ∫ R’dR’/((z 2 + R’ 2 ) ½ ) V =  /2  0 ((z 2 + R 2 ) 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), A)Its potential energy does not change B)No work is done C)Its kinetic energy does not change D)Its velocity does not change E)All of the above

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

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

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

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