$A$ wire carrying a current $i$ is placed in a uniform magnetic field $B$ in the form of the curve $y = a \sin \left( \frac{\pi x}{L} \right)$,where $0 \leq x \leq 2L$. The magnetic force on the wire is

$A, B$ and $C$ are parallel conductors of equal length carrying currents $I, I$ and $2I$ respectively. The distance between $A$ and $B$ is $x$. The distance between $B$ and $C$ is also $x$. If $F_1$ is the force exerted by $B$ on $A$ and $F_2$ is the force exerted by $C$ on $B$,choose the correct answer.

$A$ wire carrying a current $I$ is placed inside a uniform magnetic field $\vec{B} = -B_0 \hat{k}$. The shape of the wire is parabolic and has the equation $y = 2x - x^2$. The force on the wire will be:

Two long wires are hanging freely. They are joined first in parallel and then in series and then are connected with a battery. In both cases,which type of force acts between the two wires?

$A$ conducting circular loop of radius $r$ carries a constant current $i$. It is placed in a uniform magnetic field $B$,such that $B$ is perpendicular to the plane of the loop. The net magnetic force acting on the loop is

Three infinite straight wires $A, B$ and $C$ carry currents as shown in the figure. The resultant force on wire $B$ is directed: