Advanced Problems

1. A coil with 150 turns and area 0.04 m² rotates in a 0.3 T magnetic field at 100 rad/s. Calculate the maximum and average emf.
2. A bar magnet falls through a vertical coil. Determine the induced current and its direction at various positions of the magnet.
3. Two coils are placed close together. A current in coil 1 changes at 0.5 A/s. Determine the induced emf in coil 2 if mutual inductance is 0.02 H.
4. A generator produces a maximum emf of 12 V. If the coil has 60 turns and radius 0.05 m, calculate the angular speed of rotation.
5. A loop of wire experiences a sinusoidal change in magnetic flux: \(\Phi_B = 0.01 \sin(100 t)\) Wb. Find the induced emf as a function of time.
6. A coil is connected to a resistor. Using Lenz’s Law, explain the energy transformation as a magnet moves towards the coil.
7. A solenoid of length 0.5 m and 500 turns has a changing current. Determine the induced emf across the solenoid if the rate of change of current is 2 A/s and the self-inductance is 0.1 H.