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### Magnetic Fields and Forces Homework

1. A wire 0.10 m long carrying a current of 2 A is at right angles to a magnetic field. The force on the wire is 0.04 N. What is the strength of the magnetic field? What would its strength be if the wire is at an angle of 35° to the field? Ans: 0.20 T; 0.35 T
2. A wire 0.50 m long carrying a current of 8 A is at an angle of 15° to a 0.40 T field. What is the magnetic force exerted on the wire? Ans: 0.41 N
3. A beam of electrons moves at right angles to a 0.60 T field. The electrons have a velocity of 2.5 x 107 m/s. What force acts on the electrons? What force acts if the beam of electrons move at an angle of 45° to the field? Ans: 2.4 x 10-12 N; 1.7 x 10-12 N
4. A proton moves at right angles to a 0.003 T field directed out of the page. The proton moves from right to left with a speed of 5 x 106 m/s. What is the magnitude and the direction of the force the proton experiences? Ans: 2.4 x 10-15 N, towards the top of the page
5. Two parallel wires separated by 150 cm carry currents of 5 A and 15 A in opposite directions. What is the strength of the net magnetic field between the wires at a distance of 40 cm from the 5 A carrying wire? Distance is measured between the wires. Ans: 5.23 x 10-6 T
6. Repeat the previous problem for wires carrying currents in the same direction. Ans: 2.3 x 10-3 N
7. Two long, parallel wires are 10 cm apart and carry currents of 6 A and of 4 A in the same direction. Find the net strength of the magnetic field at a distance of 3 cm from the wire carrying the 6 A. Distance is measured between the wires. Ans: 2.86 x 10-5 T
8. Repeat the previous problem for currents in opposite directions. Ans: 5.14 x 10-5

### Electromagentic Induction Homework

1. A wire 0.5 m long cuts through a 0.4 T field at a speed of 20 m/s. What is the induced emf? If the wire is part of a circuit with a total resistance of 6 W, what is the current in the circuit? Ans: 4 V; 0.67 A
2. A wire 20 m long is mounted on an airplane flying at an angle of 60° to the earth's magnetic field. It flies with a speed of 120 m/s. If the induced emf is 0.12 V, what is the strength of the earth's magnetic field at this point? Ans: 5.77 x 10 -5 T
3. A step-up transformer has 200 turns on its primary and 3000 turns on its secondary. If the primary voltage is 90 V, what is the secondary voltage? If the primary current is 10 A, what is the secondary current? Ans: 1350 V; 0.67 A
4. A copper bar 30 cm long is perpendicular to a 0.8 T field and moves at right angles to the field with a speed of 0.5 m/s. Determine the emf induced in the bar. Ans: 0.12 V
5. An emf is induced in a metal rod 0.5 m long that is part of a circuit as it moves perpendicularly through a 0.15 T field at 2 m/s. The resistance of the rod and the circuit is 3 W. What is the magnitude of the induced emf? What is the current induced in the rod and the circuit? How large a force is needed to move the rod at a speed of 2 m/s? Ans: 0.15 V; 0.050 A; 3.75 x 10-3 N
6. A step-up transformer is used on a 120 V line to furnish 1800 V. The primary has 100 turns. How many turns are on the secondary? Ans: 1500 turns
7. A step-down transformer operates on a 2,500 V line and supplies a load with 80 A. The ratio of the primary turns to the secondary turns is 20:1. Determine the secondary voltage and the primary current. Ans: 125 V; 4 A