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### Magnetic Fields, Magnetic Forces, and Electromagnetic Induction Sample Problems

1. A wire 1 m long carries a current of 5 A. The wire is at right angles to a uniform magnetic field. The force on the wire is 0.2 N. What is the magnetic field strength?
2. Now in number one, the wire is directed at an angle of 30°. What is the magnetic field strength?
3. A 10 cm long wire is at right angles to a uniform magnetic field of 0.06 T. A 4 A current is in the wire. What magnetic force does it experience? What is the magnetic force if the wire was at an angle of 40° to the magnetic field?
4. A beam of electrons travels at 3,000,000 m/s through a 0.04 T field. What force does the beam experience?
5. Two currents (one of 2 A and the other of 4 A) are arranged parallel to each other, with the currents flowing in the same direction (assume they are flowing down in the plane of your paper). The wires are 3 m long and are separated by 8 cm. What is the net magnetic field at the midpoint between the two wires?
6. Repeat number five, but now the currents are flowing in opposite directions (assume the wire carrying the 2 A is flowing down and the one carrying 4 A is flowing up in the plane of your papaer).
7. Repeat number five. The wire carrying the 2 A current is to the right of the wire carrying 4 A. They are still separated by 8 cm (assume they are flowing down in the plane of your paper). What is the net magnetic field at a point 3 cm to the right of the wire carrying the 2 A current?
8. A wire 2 m long moves perpendicularly through a 0.08 T field at a speed of 7 m/s. What emf is induced? Knowing Ohm’s law and that the wire has a resistance of 0.50 ohms, what current flows?
9. The direction of a 0.045 T field is 60° above the horizontal. A wire 2.5 m long moves horizontally through this field at 2.4 m/s. What is the vertical component of the magnetic field? What emf is induced in the wire?
10. A transformer has input voltage and current of 12 V and 3 A. It has an output current of 0.75 A. If there are 1200 turns on the secondary, how many turns are on the primary? What is the input voltage?