Problem 1. A circular coil of radius 10 cm is placed in a magnetic field, the magnitude of which is varied with time as . The magnetic field is perpendicular to the plane of the coil. What is the induced emf in the coil at t = 4 s if the coil has 100 turns?

Problem 2. A circular coil of radius 20 cm is connected to a capacitor with capacitance of as shown in the figure. The coil is placed in a uniform magnetic field, the magnitude of which is varied with time as . The magnetic field is perpendicular to the plane of the coil. Find the charge of the capacitor.

Problem 3. A 20-turn circular coil surrounds a solenoid of radius 5 cm, which carries a time dependent current . The radius of the coil is 20 cm, and the coil is coaxial with the solenoid. What is the induced emf in the coil at t=1 s? The solenoid has 100 turns per centimeter.

Problem 4. A 50-turn circular coil is placed inside a solenoid, which carries a time dependent current . The radius of the coil is 5 cm, and the coil is coaxial with the solenoid. What is the induced emf in the coil at t=1 s? The solenoid has 100 turns per centimeter.

Problem 5. A conducting rail with negligible resistance slides with constant speed of 5 m/s on two parallel bars as shown in the figure. A resistor 10 ohm is connected to the bars. The distance between the bars is 10 cm and the system is placed in uniform magnetic field with magnitude of 2 T. The magnetic field is perpendicular to the plane of the rail and the bars. Find the current through the resistor.

Problem 6. A conducting rail with negligible resistance slides with constant speed of 5 m/s on two parallel bars as shown in the figure. A resistor 10 ohm and an ideal battery with voltage of 10 V are connected to the bars. The distance between the bars is 10 cm and the system is placed in uniform magnetic field with magnitude of 2 T. The magnetic field is perpendicular to the plane of the rail and the bars and pointing into the page. Find the current through the resistor.

Problem 7. A conducting rail with negligible resistance slides with constant speed of 2 m/s on two parallel bars as shown in the figure. Two resistors 10 ohm and 5 ohm are connected to the bars. The distance between the bars is 20 cm and the system is placed in uniform magnetic field with magnitude of 1 T. The magnetic field is perpendicular to the plane of the rail and the bars. Find the current through each of the resistors.

Problem 8. A 50-turn circular coil with radius of 10 cm is placed in a uniform magnetic field with the magnitude of 2 T. In the initial state the magnetic field is perpendicular to the coil. Then the coil is rotated by so that in the final state the magnetic field becomes parallel to the coil. What is the total charge, which passes through the coil? The resistance of the coil is 10 ohm.

Problem 9. A 50-turn circular coil with radius of 10 cm is placed in a uniform horizontal magnetic field with the magnitude of 2 T. In the initial state the magnetic field is perpendicular to the coil. Then the coil is rotated by about a vertical axis as shown in the figure. What is the total charge, which passes through the coil? The resistance of the coil is 10 ohm.

Problem 10. A conducting rail with the resistance of 20 ohm and mass 200 g slides down two parallel conducting rods, which are inclined at with the horizontal. The resistor 10 ohm is connected to the bars as shown in the figure. The system is placed in a uniform magnetic field directed vertically upward. Find the constant speed of the rail. The magnitude of the magnetic field is 1 T and the distance between the rods is 20 cm. Disregard the resistances of the bars.

Problem 11. In the circuit shown in the figure (a) find the current through the battery after the switch just closed; (b) find the current through the battery at the time when the switch has been closed for a long time. Assume that the battery is ideal.

Problem 12. An inductance of an LC circuit is 0.01 H and the capacitance is . At initial moment of time the capacitance is fully charged with the charge of and the current in the circuit is zero. (a) What is the frequency of electric oscillations in the circuit? (b) What is the maximum current in the circuit?

Problem 13. The maximum current in the oscillating LC circuit is 0.5 A and the maximum charge of the capacitor is . The LC circuit has 5 mH inductor. Find the capacitance of the capacitor.

Problem 14. A switch is connected to point “A” for a long time. Find the maximum current through the inductor 10 mH after the switch is thrown to point “B”.

Problem 15. A switch is connected to point “A” for a long time. Find the maximum current through the inductors after the switch is thrown to point “B”.

Problem 16. Find an equivalent inductance of the circuit between points A and B .