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Homework Problems on Faraday’s Law
Conceptual Questions (Show Fully Explanation)
1. Understanding Magnetic Flux
A circular loop of wire with radius r = 0.10 m is placed in a uniform magnetic field of 0.5 T. The normal to the loop makes an angle of 60° with the field.
(a) Calculate the initial magnetic flux through the loop.
(b) If the loop is rotated to be perpendicular to the field in 0.2 s, find the induced EMF.
Answer:
Conceptual Questions (Show Fully Explanation)
2. Faraday’s Law in a Changing Field
A rectangular coil with 100 turns and an area of 0.02 m² is placed in a uniform magnetic field of 0.3 T. The field decreases to 0 T in 0.5 s.
(a) What is the rate of change of magnetic flux?
(b) Calculate the induced EMF.
Answer:
Conceptual Questions (Show Fully Explanation)
3. Lenz’s Law and Current Direction
A bar magnet is dropped through a stationary conducting ring.
(a) Describe the direction of the induced current when the magnet approaches the ring.
(b) Describe the direction of the induced current when the magnet leaves the ring.
(c) Explain why this happens using Lenz’s Law.
Answer:
Conceptual Questions (Show Fully Explanation)
4. Motional EMF in a Moving Rod
A metal rod of length 0.5 m moves with a velocity of 3 m/s perpendicular to a uniform magnetic field of 0.2 T.
(a) Find the induced EMF across the ends of the rod.
(b) If the rod is part of a closed circuit with resistance 2 Ω, find the induced current.
Answer:
Conceptual Questions (Show Fully Explanation)
5. Application to Generators
A coil with 200 turns and an area of 0.05 m² rotates at a frequency of 50 Hz in a 0.1 T magnetic field.
(a) Derive an expression for the time-dependent EMF.
(b) Find the maximum induced EMF.
Answer:
Numerical Problems (Show Fully Explanation)
6. Induced EMF in a Solenoid
A solenoid has 500 turns per meter and carries a current of 5 A, producing a magnetic field of 0.02 T inside it. The current drops to 0 A in 0.1 s. A small coil with 10 turns and an area of 0.001 m² is placed inside the solenoid.
(a) Calculate the change in magnetic flux.
(b) Find the induced EMF in the small coil.
Answer:
Numerical Problems (Show Fully Explanation)
7. Transformer Voltage Calculation
A step-up transformer has a primary coil of 500 turns and a secondary coil of 5000 turns. The input voltage is 120 V AC.
(a) Find the output voltage.
(b) If the primary current is 5 A, find the secondary current assuming 100% efficiency.
Answer:
Numerical Problems (Show Fully Explanation)
8. Eddy Currents in a Conducting Plate
A copper plate is moving through a non-uniform magnetic field. Describe:
(a) How eddy currents are induced in the plate.
(b) Why the plate experiences a resistive force as it moves.
(c) How this principle is used in electromagnetic braking systems.
Answer:
Numerical Problems (Show Fully Explanation)
9. Magnetic Induction in a Rotating Disk
A circular aluminum disk is rotating in a uniform magnetic field.
(a) Explain why an induced EMF develops between the center and the rim.
(b) If the disk is spinning faster, what happens to the magnitude of the EMF?
(c) What happens if the magnetic field is reversed?
Answer:
Numerical Problems (Show Fully Explanation)
10. Magnetic Levitation and Lenz’s Law
A superconducting magnet is used to levitate a copper ring in mid-air.
(a) Explain how Lenz’s Law is responsible for levitation.
(b) What happens if the magnet’s strength is increased?
(c) What happens if the ring’s resistance is increased?
Answer:
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