$A$ rectangular coil $20\,cm \times 20\,cm$ has $100$ turns and carries a current of $1\,A$. It is placed in a uniform magnetic field $B = 0.5\,T$ with the direction of the magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is ........ $N-m$.

$A$ current-carrying circular loop of radius $2 \text{ cm}$ with unit normal $\hat{n} = \frac{\hat{i} + \hat{j}}{\sqrt{2}}$ is placed in a magnetic field $\vec{B} = B_0(3\hat{i} + 2\hat{j})$. If $B_0 = 4 \times 10^{-3} \text{ T}$ and current $I = 100\sqrt{2} \text{ A}$, the torque experienced by the loop is . . . . . . $\text{N}\cdot\text{m}$. $(\pi = 3.14)$

$A$ wire of length $L$ is bent in the form of a circular coil and current $i$ is passed through it. This coil is kept in a magnetic field. The torque acting on the coil will be maximum, when the number of turns is . . . . . .

$A$ circular coil of radius $9 \, cm$ carrying a current of $2 \, A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field of $\pi \times 10^{-2} \, T$. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a time period of $\frac{1}{3} \, s$. If the moment of inertia of the coil about its axis of rotation is $9 \times 10^{-5} \, kg \cdot m^2$, the number of turns of the coil is . . . . . .

$A$ square coil of side $10 \; cm$ consists of $20$ turns and carries a current of $12 \; A$. The coil is suspended vertically and the normal to the plane of the coil makes an angle of $30^{\circ}$ with the direction of a uniform horizontal magnetic field of magnitude $0.80 \; T$. What is the magnitude of torque (in $N \; m$) experienced by the coil?

$A$ rectangular coil of length $0.12\, m$ and width $0.1\, m$ having $50$ turns of wire is suspended vertically in a uniform magnetic field of strength $0.2\, Wb/m^2$. The coil carries a current of $2\, A$. If the plane of the coil is inclined at an angle of $30^{\circ}$ with the direction of the field,the torque required to keep the coil in this position will be .......$Nm$.