$A$ metallic loop is placed in a magnetic field. If a current is passed through it,then

$A$ $250$-turn rectangular coil of length $2.1\, cm$ and width $1.25\, cm$ carries a current of $85\, \mu A$ and is subjected to a magnetic field of strength $0.85\, T.$ The work done to rotate the coil by $180^o$ against the torque is .............. $\mu J$.

Four wires,each of length $2.0\,m$,are bent into four loops $P, Q, R$ and $S$ and then suspended in a uniform magnetic field. If the same current is passed in each,then the torque will be maximum on the loop:

$(a)$ $A$ current-carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around itself (i.e.,turns about the vertical axis)?
$(b)$ $A$ current-carrying circular loop is located in a uniform external magnetic field. If the loop is free to turn,what is its orientation of stable equilibrium? Show that in this orientation,the flux of the total field (external field $+$ field produced by the loop) is maximum.
$(c)$ $A$ loop of irregular shape carrying current is located in an external magnetic field. If the wire is flexible,why does it change to a circular shape?

$A$ coil in the shape of an equilateral triangle of side $l$ is suspended between the pole pieces of a permanent magnet such that $\vec{B}$ is in the plane of the coil. If due to a current $i$ in the triangle a torque $\tau$ acts on it,the side $l$ of the triangle is

$A$ circular coil of $30$ turns and radius $8.0\, cm$ carrying a current of $6.0\, A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0\, T$. The field lines make an angle of $60^o$ with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning. (in $, Nm$)