1
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1

Two coils have mutual inductance $$0.002 \mathrm{~H}$$. The current changes in the first coil according to the relation $$\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$$, where $$\mathrm{i}_0=5 \mathrm{~A}$$ and $$\omega=50 \pi$$ rad/s. The maximum value of emf in the second coil is $$\frac{\pi}{\alpha} \mathrm{~V}$$. The value of $$\alpha$$ is _______.

2
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
A $20 \mathrm{~cm}$ long metallic rod is rotated with $210~ \mathrm{rpm}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field $0.2 \mathrm{~T}$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is ____________ $\mathrm{mV}$.

Take $\pi=\frac{22}{7}$
3
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $$24 \mathrm{~cm}^{2}$$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $$12 ~\Omega$$. If an externally applied uniform magnetic field in the core along its axis changes from $$1.5 \mathrm{~T}$$ in one direction to $$1.5 ~\mathrm{T}$$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ $$\mathrm{mC}$$.

4
JEE Main 2023 (Online) 12th April Morning Shift
Numerical
+4
-1

A conducting circular loop is placed in a uniform magnetic field of $$0.4 \mathrm{~T}$$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $$1 \mathrm{~mm} / \mathrm{s}$$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $$2 \mathrm{~cm}$$ will be ___________ $$\mu \mathrm{V}$$.