## University of California, San Diego Physics 1b - Thermal Physics & Electromagnetism

 H. E. Smith Spring 2000

 Physics 1B - Tutorial #4

1. In 5 minutes, timed by your tutor, make a list of all the phenomena that you can think of that are electromagnetic in nature. Think carefully about those phenomena in which the E-M nature is hidden by charge neutrality. The group with the longest (verified!) list in each tutorial will receive gift certificates for free coffee drinks at Espresso Roma. Here's a start
1. atomic structure
2. friction (static friction, kinetic friction, viscosity, air resistance)
3. static electricity
4. lightning (big static electrical discharge!)
5. magnets
7. molecular bonds (hence chemical potential energy)
8. structure of solids
9. the fact that you don't fall through the floor (see above)
10. -  .   Since the structure of almost everyting in our world is electromagnetic in nature; virtually every phenomenon that is not identifiably nuclear or gravitational is electromagnetic in nature.

2. Metal spheres A and B, standing on insulated supports, are initially in contact with each other. Sphere C, which has a large negative charge is placed near the other spheres as shown below. While C is nearby, B is moved to the right so that the two spheres are now separated, then C is removed.
• A & B are now charged. Draw a diagram of the charge distribution on each sphere with charge sign indicated. Draw in the E-field lines between the spheres.
• If B is moved toward A, a spark is likely to jump between the spheres before they come in contact. Explain why. Where did the energy (work) for this process originate.

• When C is near A & B, positive charges are pulled toward C and negative charges are repulsed, resulting in a net (induced) positive charge on A and negative charge on B.
• When A is separated from B, and when C is removed, work is done on the system. There will be an electrical field between A & B whose strength depends upon the magnitude of the induced charge and the separation of the spheres. As A & B are moved toward each other again the field increases until it exceeds the breakdown field necessary to ionize the air between the spheres and allow charges to jump from one sphere to another - a spark - which will reduce the magnitude of the field.

3. A and B shown below are stars, of equal mass, in a binary star system. Points 1 - 5 represent small equal test masses. Draw the two forces, FA & FB on each point mass, indicating the magnitude of the force by the length of the vector. Draw the resultant vector at each point with a different colored pen.
4. A and B shown above are spherical charges of equal magnitude but opposite sign. Draw the electric fields due to the two charges, EA & EB at each point, indicating the magnitude of the field by the length of the vector. Draw the resultant vector at each point with a different colored pen.

In the diagram for 3 above, suppose A is positive and B is negative. Vectors for field due to A will point away from A.

5. Two concentric spherical conducting shells A & B (RA < RB) are charged with charges +Q and -Q respectively. Determine the Elictric Field for a) r < RA, b) RA < r < RB, c) r > rA. Draw a diagram for the E-fields.

• Inside shell A and outside shell B the field is zero: the system is spherically symmetric; net charge is zero, so by Gauss' Law, E = 0.
• Between A & B the field, E = kQ/r2 = Q/4 0 r2 - (RA < r < RB). See Hecht, p. AN-10 for a more complete explanation.

Gene Smith