The magnetic induction at any point due to a long straight wire carrying a current is

The dimension of the magnetic field intensity $B$ is

$A$ circular coil carrying a certain current produces a magnetic field $B_{0}$ at its centre. The coil is now rewound so as to have $3$ turns and the same current is passed through it. The new magnetic field at the centre is

$A$ regular polygon of $6$ sides is formed by bending a wire of length $4 \pi \text{ m}$. If an electric current of $4 \pi \sqrt{3} \text{ A}$ is flowing through the sides of the polygon,the magnetic field at the centre of the polygon would be $x \times 10^{-7} \text{ T}$. The value of $x$ is . . . . . . .

$A$ rod with a circular cross-section area $2 \text{ cm}^2$ and length $40 \text{ cm}$ is wound uniformly with $400$ turns of an insulated wire. If a current $0.4 \text{ A}$ flows in the wire winding, the total magnetic flux produced inside the winding is $4\pi \times 10^{-6} \text{ Wb}$. The relative permeability of the rod is (Given permeability of vacuum $\mu_0 = 4\pi \times 10^{-7} \text{ N m A}^{-2}$)

$A$ circular coil of wire consisting of $100$ turns,each of radius $8.0 \; cm$,carries a current of $0.40 \; A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?