Two thick wires and two thin wires,all of the same material and same length,form a square in three different ways $P, Q,$ and $R$ as shown in the figure with the current connection indicated. The magnetic field at the centre of the square is zero in cases:

$A$ 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 ..... .

Curl the palm of your right hand around the circular wire with the fingers pointing in the direction of current and the thumb gives the direction of the magnetic field. In this case,the upper side of the loop may be thought of as

$A$ $100$-turn closely wound circular coil of radius $5 \text{ cm}$ has a magnetic field of $3.14 \times 10^{-3} \text{ T}$ at its centre. The current flowing through the coil,and the magnitude of the magnetic moment of this coil are,respectively: (Take $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)

$A$ wire of length $L$ $m$ carrying a current of $I$ $A$ is bent in the form of a circle. Its magnitude of magnetic moment will be

An insulating thin rod of length $l$ has a linear charge density $\rho(x) = \rho_0 \frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin $(x = 0)$ and perpendicular to the rod. If the rod makes $n$ rotations per second,then the time-averaged magnetic moment of the rod is: