$A$ uniform magnetic field of $0.3 \; T$ is established along the positive $Z$-direction. $A$ rectangular loop in the $XY$-plane with sides $10 \; cm$ and $5 \; cm$ carries a current of $I = 12 \; A$ as shown. The torque on the loop is

$A$ rectangular coil of $400$ turns and $10^{-2} \ m^2$ area, carrying a current of $0.5 \ A$ is placed in a uniform magnetic field of $1 \ T$ such that the plane of the coil makes an angle of $60^{\circ}$ with the direction of the magnetic field. The initial moment of force acting on the coil in $Nm$ is

$A$ loop is formed by a wire of constant length carrying a current $I$ and placed in an external magnetic field $\vec{B}$. The torque $\vec{\tau}$ acting on it depends on which of the following factors?

$(a)$ $A$ 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?

$A$ closely wound solenoid of $2000$ turns and area of cross-section $1.5 \times 10^{-4} \, m^2$ carries a current of $2.0 \, A$. It is suspended through its centre and perpendicular to its length,allowing it to turn in a horizontal plane in a uniform magnetic field of $5 \times 10^{-2} \, T$ making an angle of $30^o$ with the axis of the solenoid. The torque on the solenoid will be:

$A$ solenoid of length $0.4 \ m$ and having $500$ turns of wire carries a current $3 \ A$. $A$ thin coil having $10$ turns of wire and radius $0.1 \ m$ carries current $0.4 \ A$. The torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is $(\mu_0 = 4\pi \times 10^{-7} \ SI \ units, \pi^2 = 10, \sin 90^{\circ} = 1)$.