1. Electric Potential Energy PH 203 Professor Lee Carkner Lecture 6

2. Electrical Force and Energy  Like any other force, the electrical force can do work: W = Fd = qEd   e.g. dropping a rock decreases its gravitational potential energy   U = -W = -qEd   We would like to define a quantity that tells us about the electrical energy at a point in the field that does not depend on the test charge

3. Potential Difference  The potential difference (  V) between two points is the difference in electrical potential energy between the two points per unit charge:  V = V f - V i =  U/q  V = U/q or U = Vq  Potential is the potential energy per unit charge

4. Units  Potential given in volts   Volts and Coulombs gives energy in joules  Sometimes we use electron volts (not an SI unit)   Potential is a scalar   Not a vector (like force)

5. Potential Confusion  The potential is a property of the field.   It does not depend on magnitude of the test charge   The potential energy is a property of the charge plus field (U = Vq)   Its sign depends on the sign of the charge

6. E +  Down   lose PE   “natural”  Up  lose KE   you do work   “forced”   Field is the same, but particle’s reaction is opposite Sign Convention

7. Work   Work done by the system is positive if it decreases the potential energy   Work done by the system is negative if it increases the potential energy   The negative work done by the system is the positive work done on the system  We can calculate the work from: W =  U = q  V

8. Potential and Energy   As a particle moves from an initial to a final position, energy is conserved:  K i + U i = K f + U f   If you go from high to low potential (“downhill”) a positive particle speeds up

9. Equipotentials  Equipotentials lines are drawn perpendicular to the electric field   The equipotentials for a single point charge are a series of concentric circles   Equipotentials cannot cross  This would mean the same point had two values for V

10. Calculating Potential  We know that work is the integral of force times displacement W = ∫ F dx  Relating electrical work and force F = qE V f – V i = - ∫ E ds   if E is constant  V = Ed

11. Point Charges and Potential  Consider a point charge q, what is the potential at a point a distance r away?   We can integrate from our point to infinity since V at infinity is 0  V = (1/4  0 )(q/r) 

12. Next Time  Read 24.1-24.6  Problems: Ch 24, P: 5, 7, 8, 12, 21

13. Consider three cylinders seen in cross section, each with length L and uniform charge Q, but different radii. If each is surrounded by identical Gaussian surfaces, rank the surfaces by the field at the surface, greatest first. A)a, b, c B)a, c, b C)b, a, c D)c, b, a E)All tie

14. Consider four spheres each of charge Q uniformly distributed within the volume. Point P is the same distance from the center of each sphere. Rank the situations by the field at point P, greatest first. A)a, b, c, d B)d, c, b, a C)a and b tie, c, d D)c and d tie, b, a E)All tie

15. A hollow block of metal is placed in a uniform electric field pointing straight up. What is true about the field inside the block and the charge on its top surface? A)Field inside points up, charge on top is positive B)Field inside points down, charge on top is negative C)Field inside points up, charge on top is zero D)Field inside is zero, charge on top is positive E)Field inside is zero, charge on top is zero