1. Suppose a bolt of lightning strikes the ground 5.5 m from where you are standing. If the bolt carries 28 kA of current, what is the magnitude of the lightning's magnetic field at your location? Make appropriate assumptions about the geometry of the lightning bolt.
2. Suppose the current in the lightning bolt in problem 1 decreases from 28 kA to 0.0 A in 11 μs. If you are holding a smart phone that contains a rectangular circuit with dimensions 4.2 cm by 6.1 cm and the plane of the circuit is aligned perpendicular to the magnetic field of the lightning bolt, what emf is induced in the circuit?
3. An electron moves with a speed of 12.5 km/s perpendicular to Earth's magnetic field. If the local field strength is 41 μT, what is the radius of the helical path that the electron follows?
4. A 10 km long, straight conducting cable orbits Earth in a region where the local strength of the Earth's magnetic field is 45 μT. A power supply, connected to the cable, is able to drive a current of 155 A though the cable. What is the maximum force that the magnetic field could exert on the cable?
5. A 10 cm long solenoid with 10,000 turns and a radius of 0.50 cm is connected to a battery. If the combined resistance of the solenoid and the battery is 0.80v and the magnetic field inside of the solenoid is 2.5 mT, what is the voltage of the battery?
6.At the equator, the magnetic field at the surface of the Earth is parallel to the ground and points northward. A current in a wire on the equator flows eastward. What direction does the force due to the magnetic field point?
7. A circular loop of wire with a radius of 2.0 cm and a resistance of 120 Ω is placed into a solenoid. The magnetic field in the solenoid varies from 0.10 T to 0.35 T in 0.2 ms. What current is induced in the loop?
8. If the magnetic field in the solenoid in problem 7 points toward an observer (you), which direction does the induced current flow in the loop from the observer's perspective when the field strength increases (clockwise or counterclockwise)?
9. A tiny sphere with a net charge of 2.1 μC and a mass of 2.3 μg is dropped though a 3.6 T horizontal magnetic field in a vacuum chamber. At some point, the magnitude of the magnetic force on the sphere is equal to the weight of the sphere. What is the sphere's vertical displacement when this happens, if the sphere was dropped from rest?
(Fun fact: once the sphere falls by this amount, it drifts horizontally in the g Af- B direction, making small loops as it goes).
10. A 0.5 m long wire carrying a 0.1 A current is placed parallel to another 0.5 m long wire carrying an unknown current. The wires are separated by 12 cm. If there is an attractive force of 0.81 N between the two wires,. . .
(a) What is the magnitude of the current in the second wire?
(b) Are the two currents flowing in the same direction or in opposite directions (i.e., parallel or anti-parallel)?