$A$ 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:

$A$ power line lies along the east-west direction and carries a current of $10\, A$. The force per metre due to the earth's magnetic field of ${10^{ - 4}}\, T$ is

$A$ $100$ turn rectangular coil $ABCD$ (in $xy$-plane) is hung from one arm of a balance (Figure). $A$ mass of $500 \text{ g}$ is added to the other arm to balance the weight of the coil. $A$ current of $4.9 \text{ A}$ passes through the coil and a constant magnetic field of $0.2 \text{ T}$ acting inward (in $xz$-plane) is switched on such that only arm $CD$ of length $1 \text{ cm}$ lies in the field. How much additional mass '$m$' must be added to regain the balance?

The figure shows an equilateral triangle $ABC$ of side length '$l$' carrying currents as shown,placed in a uniform magnetic field '$B$' perpendicular to the plane of the triangle. The magnitude of the net magnetic force on the triangle is:

$A$ current of $10\, A$ is flowing in a wire of length $1.5\, m$. $A$ force of $15\, N$ 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.....$^o$

Give the uses of electromagnets.