$A$ coil carrying electric current is placed in a uniform magnetic field,then

$(a)$ $A$ 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 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 . . . . . . $\mu J$.

$A$ circular loop of area $0.01\,m^2$ carrying a current of $10\,A$ is held perpendicular to a magnetic field of intensity $0.1\,T$. The torque acting on the loop is......$N-m$.

The torque required to hold a small circular coil of $10$ turns, area $1 \,mm^{2}$ and carrying a current of $\left(\frac{21}{44}\right) \,A$ in the middle of a long solenoid of $10^{3} \,turns/m$ carrying a current of $2.5 \,A$, with its axis perpendicular to the axis of the solenoid is

$A$ closely wound solenoid of $2000$ turns and area of cross-section $1.6 \times 10^{-4} \;m^{2},$ carrying a current of $4.0 \;A,$ is suspended through its centre allowing it to turn in a horizontal plane.
$(a)$ What is the magnetic moment associated with the solenoid?
$(b)$ What is the force and torque on the solenoid if a uniform horizontal magnetic field of $7.5 \times 10^{-2} \;T$ is set up at an angle of $30^{\circ}$ with the axis of the solenoid?