$A$ wire carrying a steady current $I$ is kept in the $x$-$y$ plane along the curve $y=A \sin \left(\frac{2 \pi}{\lambda} x\right)$. $A$ magnetic field $B$ exists in the $z$-direction. The magnitude of the magnetic force on the portion of the wire between $x=0$ and $x=\lambda$ is

Two straight parallel wires,both carrying $10 \ A$ in the same direction,attract each other with a force of $1 \times 10^{-3} \ N$. If both currents are doubled,the force of attraction will be:

Two long straight parallel conductors are carrying currents $i_1$ and $i_2$ in the same direction. The work done per unit length,when the distance between them is doubled,is:

$A$ large current-carrying plate is kept along the $y-z$ plane with $k \text{ A/m}$ current per unit length in the $+y$ direction. Find the net force on the semicircular current-carrying loop lying in the $x-y$ plane. The radius of the loop is $R$,the current is $i$,and the center is at $(d, 0, 0)$ where $d > R$.

$AB$ and $CD$ are smooth parallel rails,separated by a distance $l$,and inclined to the horizontal at an angle $\theta$. $A$ uniform magnetic field of magnitude $B$,directed vertically upwards,exists in the region. $EF$ is a conductor of mass $m$,carrying a current $i$. If the conductor is in equilibrium,find the relation between the given parameters.

$A$ $2 \, A$ current carrying straight metal wire of resistance $1 \, \Omega$, resistivity $2 \times 10^{-6} \, \Omega m$, area of cross-section $10 \, mm^2$ and mass $500 \, g$ is suspended horizontally in mid-air by applying a uniform magnetic field $\vec{B}$. The magnitude of $B$ is . . . . . . . $\times 10^{-1} \, T$ (given, $g=10 \, m/s^2$).