A straight wire AB of mass 40g and length 50cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude 0.40T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is _____ A. (Take g=10ms−2).
Held on 13 Apr 2023 · Verified 6 Jul 2026.
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A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 Gauss, experiences a torque of $0.016 \mathrm{~N}. \mathrm{m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$.
A small cube of side $1$ mm is placed at the centre of a circular loop of radius $10$ cm carrying a current of $2$ A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}$ J. The value of $\alpha$ is _______. ($\mu_o = 4\pi \times 10^{-7}$ Tm/A, $\pi = 3.14$)
A circular coil of radius $2$ cm and $125$ turns carries a current of $1$ A. The coil is placed in a uniform magnetic field of magnitude $0.4$ T. The axis of the coil makes an angle of $30°$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4}$ N.m. The value of $\alpha$ is ______. ($\pi=3.14$)
$1\,\mu$C charge moving with velocity $\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)$ m/s in the region of magnetic field $\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)$ T. The magnitude of force acting on it is $\sqrt{\alpha} \times 10^{-6}$ N. The value of $\alpha$ is _______.
A series LCR circuit with $R = 20\ \Omega$, $L = 1.6\text{ H}$ and $C = 40\ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ $\Omega$.
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