Electromagnetic induction is central to understanding how changing magnetic fields produce electric fields and currents — a concept that links classroom electromagnetism to real-world devices (generators, transformers, induction heating) and to many competitive-exam problems involving Faraday’s law, Lenz’s law, motional emf and Maxwell–Faraday relation. Mastery of flux, induced emf, non‑conservative induced electric fields and energy considerations is essential for board exams and for solving higher‑order JEE/NEET style multi‑step questions.
This set mixes conceptual traps, graph/data interpretation and calculation problems (including time‑dependent flux, motional emf and energy dissipation) to build problem‑solving agility. Work through each item by identifying the physical cause (motion vs transformer emf), expressing when applicable, and checking units carefully before selecting an option.
15
Minutes
10
Questions
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Marking Scheme
Q1. A rectangular conducting loop of width (side perpendicular to the direction of motion) is being pulled out of a region of uniform magnetic field at constant speed . The plane of the loop is perpendicular to the field so the flux through the portion inside the region decreases at rate . What is the magnitude of the induced emf in the loop at that instant?
Q2. A coil of turns has magnetic flux through each turn (in mWb) varying with time as
for ,
for ,
for .
What are the magnitudes of induced emf in the coil at and respectively? (Note: )
Q3. A long solenoid of radius produces a spatially uniform magnetic field inside while the external field is negligible. Using the Maxwell–Faraday relation, the magnitude of the induced azimuthal electric field (tangential to a circle of radius centered on the axis) depends on . Which option correctly gives the dependence of on (in terms of )?
Q4. Assertion (A): A straight conducting rod moving with constant velocity perpendicular to a uniform magnetic field develops a potential difference between its ends.
Reason (R): The potential difference arises because the magnetic flux through the rod changes with time.
Q5. Two parallel conducting rails separated by lie in a uniform magnetic field perpendicular to their plane. A conducting rod of length slides on the rails with constant speed while the rails are connected through a resistor . Neglecting self‑inductance, the mechanical power that must be supplied to keep the rod moving at constant speed is:
Q6. A very long solenoid of radius has a uniform magnetic field inside (external field ≈ 0). The field inside is changing at rate (constant). A single-turn circular conducting loop of radius () is placed coaxially around the solenoid. The magnitude of the induced emf in the loop is:
Q7. A thin conducting rod of length rotates about one end with angular speed in a plane perpendicular to a uniform magnetic field . What is the emf between the pivot (axis) and the free end of the rod?
Q8. A circular coil of radius has turns and resistance . A magnetic field perpendicular to its plane varies as . The amplitude of the induced current in the coil is:
Q9. Assertion (A): The induced emf in a closed conducting loop equals , where is the magnetic flux through the loop.
Reason (R): An emf is induced in a moving conductor because charges in it experience magnetic Lorentz force .
Q10. A circular coil has turns, radius and resistance . The magnetic field perpendicular to the coil varies as with . How much energy is dissipated as heat in the coil between and ?