Workshop module 8 - Physics 114, Spring 2000

1: Quickly review the concept of electromagnetic induction. Break up into 3 groups if possible. Create two or three problems for the rest of the class to figure out … be tricky! Each group should go to the board and present their problems for the class to discuss.

Group 1 should consider two circular loops lying next to each other in a plane. Current of either charge flows with a time-dependence in either direction in one of the loops. What is the direction of the induced current in the other loop?

Group 2 should do the same … except the two loops in this case are not in the same plane, rather they are coaxial with one lying near the other … like two rings on one finger.

Group 3 should consider a long, straight current carrying wire with a time–dependent current of either charge going in either direction. Around this wire they should place a circular conducting loop … in ANY orientation. What is the direction of the induced current in the loop?

2: In most parts of the northern hemisphere the earth’s magnetic field has a vertical component directed into the earth. An airplane flying east generates an emf between its wingtips. Which wingtip acquires an excess of electrons, and which a deficiency? Explain.

3: A conductor is made in the form of a hollow cylinder with inner and outer radii a and b, respectively. It carries a current I, uniformly distributed over its cross section. Derive expressions for the magnitude of the magnetic field in the regions a) r<a; b) a<r<b; c) r>b.

4: In the figure below, a rod with length L=0.0650 m moves in a magnetic field with a magnitude B=1.20 T. The emf induced in the moving rod is 0.320 V. a) What is the speed of the rod? b) If the total circuit resistance is 0.800 Ohms, what is the induced current? c) What force (magnitude and direction) does the field exert on the rod as a result of this current?

5: Two closely wound circular coils have the same number of turns, but one has twice the radius of the other. How are the self-inductances of the two coils related?

6: Two coils are wound on the same form so that the magnetic field from one coil produces flux through the turns of the second coil. When the current in the first coil is decreasing at a rate of -0.0850 A/s, the induced emf in the second coil has magnitude 7.3x10^-3 V. a) What is the mutual inductance of the pair of coils? B) If the second coil has five turns, what is the flux through each turn when the current in the first coil equals 1.60 A? c) If the current in the second coil increases at a rate of 0.0500 A/s, what is the induced emf in the first coil?

7: Now you are a pro at electromagnetic induction. When a conductor moves through a magnetic field, the magnetic forces on the charges in the conductor cause an emf. But if this phenomenon is viewed in a frame of reference moving with the conductor, there is no motion, yet there is still an emf. Okay pro … tell me how to resolve this paradox!