Electromagnetic Induction

32 solved questions from Class 12 Physics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the fundamental law or governing principle of 'Electromagnetic Induction' in Class 12 Physics? medium MCQ Fundamental Physical Law
• 2 What is the SI unit and dimensional formula for the key physical quantity studied in 'Electromagnetic Induction'? medium MCQ SI Units & Dimensional Analysis
• 3 How does the field or potential intensity vary with distance r in 'Electromagnetic Induction'? medium MCQ Spatial Distance Dependence
• 4 What is the net flux or circulation integral through a closed surface in 'Electromagnetic Induction'? medium MCQ Gauss's Theorem & Boundary Integrals
• 5 Why do field lines in 'Electromagnetic Induction' never intersect each other? medium MCQ Field Line Properties
• 6 State Faraday’s law of electromagnetic induction in its integral form. easy 1 mark Faraday’s law statement
• 7 A circular loop of radius 0.15 m rotates with constant angular speed 120 rad/s in a uniform magnetic field of 0.2 T that is perpendicular to the plane of the loop. Derive the expression for the instantaneous induced emf and compute its maximum value. hard 4 marks Induced emf in rotating loop
• 8 A coil of 50 turns has area 0.02 m² and is placed in a magnetic field of 0.5 T. The field makes an angle of 30° with the normal to the coil. If the magnetic field decreases at a rate of 0.02 T/s, what is the induced emf in the coil? medium 2 marks Faraday’s law with changing magnetic field
• 9 A square loop of side 0.10 m moves with a velocity of 2 m/s perpendicular to a uniform magnetic field of 0.05 T into a region where the field is present. What is the magnitude of the induced emf in the loop? easy MCQ 1 mark Induced emf in a moving conductor
• 10 The self‑inductance L of a long solenoid of N turns, length ℓ, cross‑sectional area A, and vacuum permeability μ_0 is given by: medium MCQ 2 marks self‑inductance of solenoid
• 11 A rectangular conducting loop of width 0.08 m and length 0.12 m moves with a constant speed v=3 m s^-1 into a region of uniform magnetic field B=0.04 T directed into the page. The plane of the loop remains parallel to the field direction. Find the magnitude of the induced emf while the loop is partially inside the field. easy 2 marks induced emf in moving conductor
• 12 Two coaxial circular coils have the same radius R=0.10 m. The first coil has N_1=200 turns and the second coil has N_2=150 turns. They are placed one directly above the other so that their planes coincide. The mutual inductance between them is M=0.12 H. If the current in the first coil varies as I_1(t)=I_0sin(200π t) A, where I_0=5 A, (i) find the maximum induced emf in the second coil, and (ii) state the direction of the induced current at the instant when I_1 is increasing through zero. hard 4 marks mutual inductance and induced emf
• 13 State Lenz’s law. A conducting rod of length 0.50 m slides down smooth inclined rails that make an angle 30° with the horizontal. The rails and the rod form a closed rectangular circuit in a uniform magnetic field B=0.20 T directed into the page. Indicate the direction of the induced current in the rod when it is moving downwards. easy 1 mark Lenz’s law and direction of induced current
• 14 Two coaxial circular coils each have a radius of 0.05,m. Coil 1 has 180 turns and Coil 2 has 120 turns. The mutual inductance between them is 0.08,H. If the current in Coil 1 varies as I_1(t)=4sin(500π t),A, (i) find the maximum magnitude of the induced emf in Coil 2, and (ii) state the direction of the induced current when I_1 is increasing through zero. medium 3 marks Mutual inductance and induced emf
• 15 A long solenoid has a length of 0.6,m, cross‑sectional area 5×10^-4,m^2, and N turns. It is placed in a uniform magnetic field of 0.2,T which is suddenly switched off at t=0. The current in the solenoid changes from 10,A to 0,A in 0.02,s. If a secondary coil of 100 turns is wound around the solenoid, find the induced emf in this coil. Assume the solenoid is long enough that its self‑inductance can be approximated as L=μ_0N^2A/ℓ. hard 5 marks Self‑inductance of a solenoid and induced emf
• 16 A rectangular loop of dimensions 0.20,m×0.10,m rotates with a constant angular velocity of 250,rad s^-1 in a uniform magnetic field of 0.30,T that is perpendicular to the axis of rotation. The loop is initially positioned with its plane parallel to the field. (i) Derive an expression for the instantaneous induced emf. (ii) Determine the maximum value of the induced emf. hard 4 marks Faraday’s law for rotating loop
• 17 A straight conducting wire of length 0.30,m moves with a constant velocity of 4,m s^-1 perpendicular to a uniform magnetic field of 0.15,T directed into the page. Find the magnitude of the induced emf across the ends of the wire. easy 2 marks Motional emf in a moving conductor
• 18 A rectangular coil of N = 50 turns, each turn having an area A = 0.020 m^2, rotates with a constant angular speed ω = 150 rad s^-1 in a uniform magnetic field B = 0.30 T that is perpendicular to the axis of rotation. What is the maximum emf induced in the coil? medium MCQ 2 marks Induced emf in a rotating coil
• 19 Two long solenoids share the same axis. The primary solenoid has N_1=200 turns, the secondary has N_2=150 turns, and their mutual inductance is M=0.05 H. If the current in the primary decreases uniformly from 3 A to 0 A in 0.010 s, (i) calculate the magnitude of the emf induced in the secondary, and (ii) state the direction of the induced current relative to the original current in the primary. medium 2 marks Mutual inductance and Lenz’s law
• 20 An RL circuit consists of a resistor R = 20 Ω and an inductor L = 0.50 H. At t=0 a constant emf E=10 V is applied across the series combination. Find the time required for the current to reach 90% of its steady‑state value. hard 4 marks Time constant of an RL circuit
• 21 A straight conducting rod of length 0.40 m slides on smooth horizontal rails with a constant speed v = 5 m s^-1 perpendicular to a uniform magnetic field B = 0.20 T directed into the page. Find the magnitude of the induced emf across the ends of the rod. easy 1 mark Motional emf in a moving conductor
• 22 A rectangular coil of N=100 turns has length l=0.15 m and width w=0.10 m (area A=0.015 m^2). It rotates with constant angular speed ω=200 rad s^-1 about an axis that makes an angle θ=30° with a uniform magnetic field B=0.40 T. (i) Write the expression for the instantaneous induced emf. (ii) Calculate its maximum value. medium 3 marks Rotating coil (alternating emf)
• 23 Two coaxial circular coils share the same axis. The primary coil has N_1=200 turns, the secondary coil has N_2=150 turns, and their mutual inductance is M=0.06 H. The current in the primary varies sinusoidally as I_1(t)=5cos(120π t) A. (i) Find the maximum magnitude of the emf induced in the secondary coil. (ii) State the direction of the induced current at an instant when the primary current is decreasing. hard 4 marks Mutual induction and Lenz’s law
• 24 In a series RL circuit a constant emf E=5 V is applied across a resistor R=10 Ω and an inductor L (unknown). The current after t=0.20 s is measured to be 0.30 A. Find the self‑inductance L of the circuit. easy 2 marks Self‑induction (time constant)
• 25 A straight conducting rod of length 0.60 m moves with a constant speed of 4.0 m s\textsuperscript{-1} perpendicular to a uniform magnetic field of magnitude 0.30 T directed into the page. Find the magnitude of the induced emf across the ends of the rod. easy 2 marks Faraday’s law for motional emf
• 26 Two long coaxial solenoids share the same axis. The primary solenoid has 250 turns and the secondary has 180 turns. Their mutual inductance is 0.09 H. If the current in the primary decreases linearly from 5 A to 0 A in 0.004 s, (i) calculate the magnitude of the emf induced in the secondary coil, (ii) state the direction of the induced current in the secondary relative to the direction of the primary current just before it started to decay. hard 4 marks Mutual inductance and Lenz’s law
• 27 A series RL circuit is driven by a constant emf of 12 V. The resistor has resistance 8 Ω and the inductor has self‑inductance L (unknown). At t=0.10 s after the emf is applied, the current through the circuit is measured to be 1.2 A. Find the value of L. medium 3 marks Inductive time constant and current growth
• 28 A circular coil of 200 turns has radius 0.05 m and is rotating with constant angular speed 120 rad s\textsuperscript{-1} about an axis that makes an angle of 45° with a uniform magnetic field of 0.20 T that is perpendicular to the coil's plane. (i) Write the expression for the instantaneous induced emf. (ii) Calculate its maximum value. medium 3 marks Faraday’s law with rotating coil at oblique angle
• 29 Two coaxial circular coils share the same axis. Coil 1 has N_1=250 turns, coil 2 has N_2=180 turns and their mutual inductance is M=0.07 H. The current in coil 1 varies as I_1(t)=3sin(2π×60 t) A.\n(i) Find the maximum magnitude of the emf induced in coil 2.\n(ii) At the instant when I_1 is increasing through zero, state the direction of the induced current in coil 2 relative to the direction of the current that would be produced in coil 1 by the same instantaneous emf. hard 4 marks Mutual inductance and Lenz’s law
• 30 A rectangular coil of N=120 turns, length l=0.25 m and width w=0.15 m, rotates with constant angular speed ω=180 rad s^-1 about an axis that makes an angle α=60° with a uniform magnetic field B=0.35 T. (i) Write the expression for the instantaneous emf induced in the coil. (ii) Calculate the maximum emf value. hard 3 marks Rotating rectangular coil (alternating emf)
• 31 A straight conducting rod of length 0.25 m moves with a speed 3.0 m s^-1 perpendicular to a uniform magnetic field of 0.40 T directed into the page. Find the magnitude of the induced emf across the ends of the rod. easy 1 mark Motional emf (Faraday’s law)
• 32 In a series RL circuit a constant emf E=15 V is applied at t=0. The resistor has R=5 Ω and the current after 0.20 s is 2.0 A. What is the self‑inductance L of the circuit? medium MCQ 2 marks Transient current in RL circuit