A non conducting ring (of mass $m,$ radius $r,$ having charge $Q$) is placed on a rough horizontal surface (in a region with transverse magnetic field). The field is increasing with time at the rate $R$ and coefficient of friction between the surface and the ring is $\mu .$ For ring to remain in equilibrium $\mu$ should be greater than

Wires $1$ and $2$ carrying currents ${i_1}$ and ${i_2}$respectively are inclined at an angle $\theta $ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$

A rectangular coil $20\,cm \times 20\,cm$ has $100$ $turns$ and carries a current of $1\, A$. It is placed in a uniform magnetic field $B =0.5\, T$ with the direction of magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is........$N-m$

$AB$ 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 $B$ is normal to the plane of the rails

A wire is bent in the form of an equilateral triangle of side $100 \,cm$ and carries a current of $2 \,A$. It is placed in a magnetic field of induction $2.0 \,T$ directed perpendicular into the plane of paper. The direction and magnitude of magnetic force acting on each side of the triangle will be

Define $\mathrm{SI}$ unit of electric charge in terms of Ampere.