$A$ long straight rod of diameter $4 \text{ mm}$ carries a steady current '$i$'. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances $1 \text{ mm}$ and $4 \text{ mm}$ from the axis of the rod is

The magnetic field due to a current-carrying loop of radius $3 \text{ cm}$ at a point on its axis at a distance of $4 \text{ cm}$ from its centre is $54 \mu\text{T}$. Then,the value of the magnetic field at the centre of the loop is: (in $\mu\text{T}$)

Give two different properties of a current-carrying coil and state Ampere's suggestion.

For the adjoining figure,the magnetic field at point $P$ will be:

$A$ current of $1\,A$ is passed through a hexagonal conducting wire of side $1\,m$. The magnetic induction at its centre $O$ in $Wb/m^2$ will be

$A$ current-carrying loop $ABCD$ has two circular arcs $AD$ and $BC$ with radii $1 \text{ cm}$ and $2 \text{ cm}$ respectively, as shown in the figure. The two arcs $AD$ and $BC$ subtend a common angle of $30^{\circ}$ at the centre $O$. If the current flowing in the loop is $\frac{1.2}{\pi} \text{ A}$, then the magnitude of the net magnetic field at $O$ is (Given $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$): (in $\mu \text{T}$)