$A$ straight current-carrying conductor is kept along the axis of a circular loop carrying current. The force exerted by the straight conductor on the loop is

$A$ thin uniform rod with negligible mass and length $l$ is attached to the floor by a frictionless hinge at point $P$. $A$ horizontal spring with force constant $k$ connects the other end to a wall. The rod is in a uniform magnetic field $B$ directed into the plane of the paper. What is the extension in the spring in equilibrium when a current $i$ is passed through the rod in the direction shown? Assume the spring is initially at its natural length.

$A$ loop of flexible conducting wire lies in a magnetic field of $2.0 \,T$ with its plane perpendicular to the field. The length of the wire is $1 \,m$. When a current of $1.1 \,A$ is passed through the loop, it opens into a circle. The tension developed in the wire is (in $\,N$)

Three long straight wires are connected in parallel to each other across a battery of negligible internal resistance. The ratio of their resistances is $3 : 4 : 5$. What is the ratio of the distances of the middle wire from the others if the net force experienced by it is zero?

The figure shows a conducting loop $ADCA$ carrying current $i$ and placed in a region of uniform magnetic field $B_0$. The part $ADC$ forms a semicircle of radius $R$. The magnitude of the force on the semicircular part of the loop is equal to

$A$ 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: