$A$ square loop of side $l$ is placed in the neighbourhood of an infinitely long straight wire carrying a current $I_1$. The loop carries a current $I_2$ as shown in the figure.

$A$ steady current $i$ flows in a small square loop of wire of side $L$ in a horizontal plane. The loop is now folded about its middle such that half of it lies in a vertical plane. Let $\overrightarrow {{\mu _1}} $ and $\overrightarrow {{\mu _2}} $ respectively denote the magnetic moments due to the current loop before and after folding. Then

An electron in a circular orbit of radius $0.05 \ nm$ performs $10^{16}$ revolutions per second. The magnetic moment due to this rotation of the electron is (in $A \ m^{2}$):

$A$ thin circular disk of radius $R$ is uniformly charged with surface charge density $\sigma > 0$. The disk rotates about its central axis with a uniform angular speed $\omega$. The magnetic moment of the disk is:

The magnetic moment vectors $\mu_{s}$ and $\mu_{l}$ associated with the intrinsic spin angular momentum $S$ and orbital angular momentum $L$ respectively,of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by $\mu_{s} = -(e/m)S$ and $\mu_{l} = -(e/2m)L$. Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

Two circular concentric loops of radii $r_1 = 20\,cm$ and $r_2 = 30\,cm$ are placed in the $X, Y-$ plane as shown in the figure. $A$ current $I = 7\,A$ is flowing through them in opposite directions. The magnetic moment of this loop system is