NEET Electromagnetic Induction MCQs & PYQs

Assertion (A) is true based on Faraday's Law, which states that induced current is generated only by a change in magnetic flux. Reason (R) is false because a constant magnetic flux, regardless of its magnitude, does not induce a current.

The mutual inductance is given by \(M = k \sqrt{L_1 L_2}\). If \(L_1\) and \(L_2\) are doubled, the new mutual inductance becomes \(M' = k \sqrt{(2L_1)(2L_2)} = 2k \sqrt{L_1 L_2} = 2M\). Thus, (A) is true and (R) correctly explains (A).

Assertion (A) is false; a charged particle released from rest experiences no magnetic force (\(F_B = q(v \times B)\)). While an induced electric field exists, it does not necessarily cause circular motion. Reason (R) is false; a time-varying magnetic field induces a non-conservative electric field.

Assertion (A) is true, as mutual inductance \(M\) depends on the self-inductances \(L_1\) and \(L_2\) (\(M \le \sqrt{L_1 L_2}\)). Reason (R) is false; if two coils are perfectly uncoupled (\(k=0\)), their mutual inductance is zero, but their self-inductances \(L_1\) and \(L_2\) can still be non-zero.

Assertion (A) is true: The induced EMF is \(emf = -L \frac{dI}{dt}\). Even if \(I=0\) instantaneously, \(frac{dI}{dt}\) can be non-zero (e.g., during oscillation or switching). Reason (R) is true, describing Lenz's law. However, R is not the correct explanation for A, as A focuses on instantaneous values of \(I\) and \(frac{dI}{dt}\).

From induced emf \(e = L \frac{di}{dt}\), we have \(L = \frac{e dt}{di}\). Thus, the unit of inductance (henry) is equivalent to \(\frac{\text{Volt-second}}{\text{Ampere}}\).

The induced emf is given by \(e = BA\omega \sin\theta\). Given \(e = \frac{\sqrt{3}}{2}BA\omega\), we have \(\sin\theta = \frac{\sqrt{3}}{2}\), which yields \(\theta = \frac{\pi}{3}\).

Efficiency \(\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100% = \frac{50}{220 \times 1/4} \times 100% = \frac{50}{55} \times 100% \approx 91%\).

The magnetic field at the center of the outer coil of radius \(R\) carrying current \(I\) is \(B = \frac{\mu_0 I}{2R}\). The flux through the inner coil of radius \(r\) is \(\Phi = B \cdot (\pi r^2) = \frac{\mu_0 \pi r^2 I}{2R}\). Thus, \(M = \frac{\Phi}{I} = \frac{\mu_0 \pi r^2}{2R}\).

Diamagnetism is an intrinsic property arising from the orbital motion of electrons and does not involve the alignment of permanent atomic dipoles against thermal agitation. Hence, its susceptibility is independent of temperature.