$A$ coil carrying a heavy current and having a large number of turns is mounted in a $N-S$ vertical plane,and a current flows in a clockwise direction. $A$ small magnetic needle at its center will have its north pole in:

$A$ closely wound solenoid of $800$ turns and area of cross section $2.5 \times 10^{-4} \text{ m}^2$ carries a current of $3.0 \text{ A}$. The magnetic moment associated with it is . . . . . . . (in $\text{ JT}^{-1}$)

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.

$A$ current carrying wire of length $L$ is transformed into a coil of $N$ turns. To achieve maximum magnetic moment,the coil

$A$ current loop placed in a magnetic field behaves like a

$A$ uniform conducting wire of length $24a$ and resistance $R$ is wound up as a current-carrying coil in the shape of an equilateral triangle of side $a$ and then in the form of a square of side $a$. The coil is connected to a voltage source $V_{0}$. The ratio of the magnetic moment of the coils in the case of the equilateral triangle to that of the square is $1 : \sqrt{y}$, where $y$ is ..... .