$A$ wire carrying current $I$ along the $x$-axis has length $\ell$ and is kept in a magnetic field $\vec{B} = (\hat{i} + 2\hat{j} - 3\hat{k}) B \text{ Wb/m}^2$. The magnitude of the magnetic force acting on the wire is:

For the circuit shown in the figure,the direction and magnitude of the force on the segment $PQR$ is:

$A$ current-carrying rectangular loop is placed near a straight infinitely long current-carrying wire as shown in the figure. The torque acting on the loop is

$A$ long straight wire is carrying current $I_1$ in the $+z$ direction. The $x-y$ plane contains a closed circular loop carrying current $I_2$ and does not encircle the straight wire. The net force on the loop will be:

$A$ straight wire is placed in a magnetic field that varies with distance $x$ from the origin as $\vec{B} = B_0 \left( 2 - \frac{x}{a} \right) \hat{k}$. The ends of the wire are at $(a, 0)$ and $(2a, 0)$ and it carries a current $I$ in the positive $x$-direction. If the force on the wire is $\vec{F} = IB_0 \left( \frac{ka}{2} \right) \hat{j}$, then the value of $k$ is:

The force on a current-carrying loop (radius $= R$) in a uniform magnetic field $(B)$,which is at an angle $30^{\circ}$ with the normal,will be: