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

$A$ straight wire of mass $0.2 \,kg$ and length $1.5 \,m$ carries a current of $2 \,A$, as shown in the figure. It is suspended in mid-air by a uniform magnetic field $B$ pointing into the plane of the paper. Calculate the magnitude of the magnetic field. (Ignore Earth's magnetic field and assume $g = 10 \,m/s^2$) (in $\,T$)

$A$ straight wire $AB$ of mass $40\,g$ and length $50\,cm$ is suspended by a pair of flexible leads in a uniform magnetic field of magnitude $0.40\,T$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........$A$. (Take $g=10\,ms^{-2}$).

$A$ long current-carrying conductor is placed near a rectangular current loop as shown in the figure. Calculate the resultant force on the current loop.

Three long straight wires are carrying current as shown in the diagram. The magnetic force per unit length on wire $Q$ is $..... \times 10^{-7} \ N/m$.

$A$ current of $5 \ A$ is flowing in a wire of length $1.5 \ m$. $A$ force of $7.5 \ N$ acts on it when it is placed in a uniform magnetic field of $2 \ T$. The angle between the magnetic field and the direction of the current is......$^o$