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

Two parallel wires in free space are $10\, cm$ apart and each carries a current of $10\, A$ in the same direction. The force one wire exerts on the other per metre of length is

Obtain equation for force between two parallel currents carrying wire.

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

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

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