$A$ square loop of edge length $2 \ m$ carrying current of $2 \ A$ is placed with its edges parallel to the $x-y$ axis. $A$ magnetic field is passing through the $x-y$ plane and expressed as $\vec{B}=B_0(1+4x) \hat{k}$,where $B_0=5 \ T$. The net magnetic force experienced by the loop is . . . . . . $N$.

$A$ and $B$ are two conductors carrying a current $i$ in the same direction. $x$ and $y$ are two electron beams moving in the same direction.

$A$ horizontal rod of mass $10 \, g$ and length $10 \, cm$ is placed on a smooth plane inclined at an angle of $60^\circ$ with the horizontal,with the length of the rod parallel to the edge of the inclined plane. $A$ uniform magnetic field of induction $B$ is applied vertically downwards. If the current through the rod is $1.73 \, A$,then the value of $B$ for which the rod remains stationary on the inclined plane is......$T$

Two long wires carrying currents $I_1$ and $I_2$ are arranged as shown in the figure. The wire carrying current $I_1$ is along the $x$-axis. The other wire carrying current $I_2$ is parallel to the $y$-axis,passing through the point $(0, 0, d)$. Find the magnetic force exerted on a segment of length $dl$ of the second wire at the point $O_2(0, 0, d)$ due to the wire carrying current $I_1$.

The wires which connect the battery of an automobile to its starting motor carry a current of $300\; A$ (for a short time). What is the force per unit length between the wires if they are $70\; cm$ long and $1.5\; cm$ apart? Is the force attractive or repulsive?

$A$ metal ring of radius $r = 0.5 \, m$ with its plane normal to a uniform magnetic field $B$ of induction $0.2 \, T$ carries a current $I = 100 \, A$. The tension in newtons developed in the ring is: