Electromagnetic induction is central to both CBSE board questions and competitive exams (JEE/NEET) because it links fundamental laws (Faraday's and Lenz's) with practical devices — generators, transformers, eddy-current brakes — and tests a student's ability to move between qualitative Lenz-law reasoning and quantitative flux-rate computations. Mastery of this chapter sharpens skills in calculus-based flux evaluation, sign conventions, non-conservative induced electric fields and energy considerations that frequently appear in higher-weight problems.
Competitions emphasize multi-step reasoning: setting up flux as a function of geometry/time, differentiating correctly, interpreting piecewise graphs or data, and connecting induced emf to work, power and energy. The following 10-item practice set (board + JEE/NEET level) focuses on these skills: numerical calculation, graph/data interpretation, tricky conceptual traps and assertion–reason reasoning typical of CBSE format.
15
Minutes
10
Questions
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Marking Scheme
Q1. A conducting rod of length slides without friction on two parallel conducting rails separated by distance . The rails are connected by a resistor to form a closed rectangular circuit. The assembly lies in a uniform magnetic field directed into the page. The rod is pulled to the right with constant speed . The magnitude of the magnetic retarding force on the rod is:
Q2. A square loop of side and resistance is being pulled out of a region of uniform magnetic field (into the page) at constant speed . The side crosses the boundary so the area inside the field decreases at rate . At the instant when half the loop is inside the field, the magnitude of the induced current in the loop is:
Q3. The magnetic flux through a single-turn loop varies with time as follows: from to it increases linearly from to ; from to it remains constant at ; from to it decreases linearly to . The magnitude of the induced emf at is:
Q4. A single-turn circular conducting loop of radius and resistance is placed in a magnetic field perpendicular to its plane. The field decays from to zero (time-dependence not needed). The total charge that flows around the loop during the entire process is:
Q5. A coil of turns and area rotates with angular speed in a uniform magnetic field with its axis perpendicular to the field. The amplitude of the induced emf in the coil is:
Q6. Assertion (A): If the magnetic flux through a loop decreases linearly with time, say with , the magnitude of the induced emf in the loop remains constant.
Reason (R): The induced emf is proportional to the second time derivative of flux, i.e. .
Q7. The current in a primary coil varies as follows: from to it increases linearly from to ; from to it stays at ; from to it decreases linearly to . A secondary coil coaxial with the primary has mutual inductance . The magnitude of the induced emf in the secondary at is:
Q8. A conducting disc of radius rotates with angular speed about its axis (perpendicular to the disc). A magnetic field normal to the disc varies with radius as where is the field at the rim. The magnitude of the emf between centre and rim is:
Q9. Assertion (A): The electric field induced by a time-varying magnetic field is conservative and can be expressed as the gradient of a scalar potential.
Reason (R): Faraday's law states , which can be non-zero for changing flux; hence the induced electric field is, in general, non-conservative.
Q10. A conducting rod of length slides without friction on parallel rails forming a closed circuit with resistance . The rod moves in a uniform magnetic field normal to the loop. Its speed decays as with and . The total energy dissipated as heat in the resistor from to is: