$A$ particle of mass $m$ and charge $Q$ moving with a speed $v$ in a circular path of radius $R$ has a magnetic moment $\mu$. If the mass of the particle is doubled and it maintains the same speed while revolving in the same circular path, then the magnetic moment will be

$A$ 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 ..... .

Magnetic induction at the centre of a circular loop of area $\pi \ m^2$ is $0.1 \ T$. The magnetic moment of the loop is ( $\mu_0 = \text{permeability of air}$ ).

An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_A = 10 \ cm$ and $r_B = 20 \ cm$ respectively are equal. If $N_A, I_A$ and $N_B, I_B$ are the number of turns and current of $A$ and $B$ respectively,then which of the following relations is correct?

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