Some additional concept questions to help you review:
- A proton is sitting motionless in a uniform magnetic field. I turn an electric field on for 10 seconds, that points in the same direction as the magnetic field. After the electric field is turned off, what does the motion of the proton look like?
Answer: The electric field accelerates the proton in the direction of the electric field, which is also the direction of the magnetic field. Thus the proton is moving with constant velocity in this direction after the electric field is turned off. Since the magnetic field is in the same direction as the velocity, the proton feels no magnetic force, so it moves with constant speed and direction.
- I repeat the above experiment, but this time the electric field points in a direction perpendicular to the magnetic field. After I turn the electric field off, what does the motion of the proton look like?
Answer: In this case, the proton acquires some velocity perpendicular to the magnetic field, so after the electric field is turned off the proton moves in a circle within the magnetic field.
- Infamous Fig 21.28a shows two wires with currents in opposite directions. They each feel a repulsive force. Let’s assume the currents are equal. Is it possible to put a third wire in between them, with a current through the third wire, so as to cancel out the repulsive forces each of them feel?
Answer: The magnetic field caused by wire 1 on wire 2 points upwards. The magnetic field caused by wire 2 on wire 1 also points upwards. It is impossible to place a third wire in between so as to cancel out both these fields; the field from a 3rd wire in the middle will point one direction at wire 1 and the opposite direction at wire 2.
- What about in Fig. 21.28b, with the currents in the same direction? Now the original two wires are feeling an attractive force; can we put a third wire between them to cancel out this attraction?
Answer: In this case, it will work, with similar reasoning as the previous question. Now the field from wire 2 acting on wire 1 points downward. So, a third wire in the middle with a current in the opposite direction as the two wires will cause a repulsive force acting on the original two wires. If the current is adjusted on this 3rd wire, you can cancel out the original attractive forces. Note that the current on this 3rd wire that would do this is not as large as the original currents.
- If you have an isolated loop of wire with current through it, and there is no external magnetic field, the loop of wire feels no net force and no net torque. Yet, the loop of wire itself is generating a magnetic field, as discussed in section 21.7. Explain why the magnetic field the loop of wire generates does not create a net force or a net torque on the loop. Probably the simplest way to explain it is to use a rectangular loop.
Answer: If you draw out a loop, you will find that the sides of the loop exert equal and opposite forces on each other. Thus, there is no net force. All of the forces act in the plane of the loop, thus there is no force perpendicular to the loop which would generate a torque.