The ratio of the magnetic field at the centre of a current-carrying circular coil to its magnetic moment is $\alpha$. If the current and radius both are doubled,then the new ratio will become:

$A$ closely wound solenoid of $800$ turns and area of cross-section $2.5 \times 10^{-4} \; m^2$ carries a current of $3.0 \; A$. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

$A$ coil of $n$ turns and radius $R$ carries a current $I$. It is unwound and rewound to make a new coil of radius $\frac{R}{3}$ and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil is

In an atom,an electron of charge $(-e)$ performs uniform circular motion ($U$.$C$.$M$.) around a stationary positively charged nucleus with a period of revolution $T$. If $r$ is the radius of the orbit of the electron and $v$ is the orbital velocity,then the circulating current $I$ is proportional to:

$A$ charge $q$ is spread uniformly over an isolated ring of radius $R$. The ring is rotated about its natural axis with an angular velocity $\omega$. Magnetic dipole moment of the ring is

$A$ wire of length $L \ m$ carrying a current $I \ A$ is bent in the form of a circle. The magnitude of its magnetic moment is