The magnetic field existing in a region is given by $\vec{B} = B_0 \left(1 + \frac{x}{l}\right) \hat{k}$. $A$ square loop of edge length $l$ and carrying a current $i$ is placed with its edges parallel to the $x$ and $y$ axes. Find the magnitude of the net magnetic force experienced by the loop.

$A$ semi-circular current-carrying wire having radius $R$ is placed in the $x-y$ plane with its centre at the origin $O$. $A$ non-uniform magnetic field $\vec B = \frac{B_o x}{2R} \hat k$ (where $B_o$ is a positive constant) exists in the region. The magnetic force acting on the semi-circular wire will be along:

$A$ conductor lies along the $z$-axis in the range $-1.5 \le z < 1.5 \ m$ and carries a fixed current of $10.0 \ A$ in the $-\hat{a}_z$ direction (see figure). For a magnetic field $\vec{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_y \ T$,find the power required to move the conductor at a constant speed to $x = 2.0 \ m, y = 0 \ m$ in $5 \times 10^{-3} \ s$. Assume parallel motion along the $x$-axis.

Two parallel wires $1 \text{ m}$ apart carry currents of $1 \text{ A}$ and $3 \text{ A}$ respectively in opposite directions. The force per unit length acting between these two wires 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

$A$ wire carrying current $I$ along the $x$-axis has length $\ell$ and is kept in a magnetic field $\vec{B} = (\hat{i} + 2\hat{j} - 3\hat{k}) B \text{ Wb/m}^2$. The magnitude of the magnetic force acting on the wire is: