The magnetic field at the center of a circular coil of radius $0.1\, m$ having $1000$ turns and carrying a current of $0.1\, A$ is:

Two infinitely long thin wires are placed at $(1 \text{ cm}, 0 \text{ cm})$ and $(2 \text{ cm}, 0 \text{ cm})$ as shown in the figure. The same current $i$ flows in both the wires in the same direction,into the page. Let the magnetic field at the origin due to these wires be $\vec{B}$. If $B_0$ is the magnitude of the magnetic field if only the wire at $(1 \text{ cm}, 0 \text{ cm})$ was present,then the value of $B / B_0$ is

Magnetic field intensity at the centre of a coil of $50$ turns,radius $0.5\, m$ and carrying a current of $2\, A$ is:

In terms of basic units of mass $(M)$,length $(L)$,time $(T)$ and charge $(Q)$,the dimensions of magnetic permeability of vacuum $(\mu_0)$ would be

$A$ and $B$ are two concentric circular loops carrying currents $i_1$ and $i_2$ as shown in the figure. If the ratio of their radii is $1:2$ and the ratio of the magnetic flux densities at the centre $O$ due to $A$ and $B$ is $1:3$,then the value of $\frac{i_1}{i_2}$ will be

$A$ wire in the form of a square of side $a$ carries a current $i$. Then,the magnetic induction at the centre of the square is (Magnetic permeability of free space $= \mu_0$)