A square loop of mass $m$ and side $a$, carries a current $i$ and placed on a horizontal table, in a magnetic field $\overrightarrow{B}$ which is at an angle of $\mathrm{\theta }$ with the vertical axis, as shown in the figure. If $m=500 \mathrm{gm}, a=0.5 \mathrm{m}, B=2 \mathrm{T}$ and $\mathrm{\theta }$$={30}^{\circ }$ from vertical, find the minimum magnitude of current (in $\mathrm{ampere}$) so that the loop topples.

The rectangular coil having $100$ turns is turned in a uniform magnetic field of $\frac{0.05}{\sqrt{2}} \hat{\mathrm{j}} \mathrm{T}$, as shown in the figure. The torque acting on the loop is

If a wire of $6.28 \mathrm{m}$ length is converted into two semicircular loops of same radius, as shown in the figure, then the magnetic force on the wire will be

A conducting wire $PQRSTU$ is turned, as shown in the figure. The length of each segment is $\mathrm{l}$ and a current $i$ is flowing through it. If it is placed in a uniform magnetic field $B$, directed along $Y$ axis, then the force acting on the wire will be

A current carrying loop is placed in a uniform magnetic field in four different orientations. Arrange them in decreasing order of their potential energy.

(a) 

(b)

(c)

(d) 

Three long current carrying wires, $P, Q$ and $R$, are placed perpendicular to the plane of a paper. Magnetic force per unit length, on the wire $R$, is

A current carrying loop is placed in a uniform magnetic field, as shown. The torque on the loop is 

Four wires, of equal length, are bent in the form of four loops, $P, Q, R$ and $S$. They are suspended in a uniform magnetic field and same current is passed through them. The maximum torque will act on