The ratio of the magnetic field and the magnetic moment at the centre of a current-carrying circular loop is $x$. When both the current and the radius are doubled, the ratio will be:

In the given diagram,a rod is rotating with angular velocity $\omega$. The mass of this rod is $m$,the charge is $q$,and the length is $l$. Find the magnetic moment of this rod.

$A$ straight wire carrying current $i$ is turned into a circular loop. If the magnitude of the magnetic moment associated with it in $MKS$ units is $M$,the length of the wire will be

$A$ current-carrying loop consists of $3$ identical quarter circles of radius $R$,lying in the positive quadrants of the $xy$,$yz$,and $zx$ planes with their centers at the origin,joined together. Find the direction and magnitude of the magnetic field $\vec{B}$ at the origin.

$A$ 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 ..... .

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