$A$ wire of length $L$ is bent in the form of a circular coil and current $i$ is passed through it. This coil is kept in a magnetic field. The torque acting on the coil will be maximum, when the number of turns is . . . . . .

In the figure shown,a coil of single turn is wound on a sphere of radius $R$ and mass $m$. The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. The current in the coil is $i$. If the sphere is in equilibrium,the value of the magnetic field $B$ is:

$(a)$ $A$ 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?

$A$ current-carrying coil is subjected to a uniform magnetic field. The coil will orient itself so that its plane becomes

Two identical conducting wires $A$ and $B$ of same dimensions and same material are bent in the form of circular coils. Wire $A$ consists of a single turn,whereas wire $B$ consists of $2$ turns. Both these wires are then suspended in a uniform magnetic field with their planes parallel to one another,and the same current is passed through them. Which statement is correct?

$A$ coil having $100$ turns, area of $5 \times 10^{-3} \, m^2$, carrying current of $1 \, mA$ is placed in a uniform magnetic field of $0.20 \, T$ such that the plane of the coil is perpendicular to the magnetic field. The work done in turning the coil through $90^{\circ}$ is . . . . . . $\mu J$.