$A$ circular coil $A$ has a radius $R$ and the current flowing through it is $I$. Another circular coil $B$ has a radius $2R$ and the current flowing through it is $2I$. The ratio of the magnetic fields at the centre of the circular coils $(B_A : B_B)$ is: (in $:1$)

$A$ current of $5 \; A$ flows through a square loop of side length $\frac{1}{\sqrt{2}} \; m$. The magnitude of the magnetic field $B$ at the centre of the square loop is $p \times 10^{-6} \; T$. Find the value of $p$. [Take $\mu_0 = 4 \pi \times 10^{-7} \; T \cdot m \cdot A^{-1}$].

$A$ horizontal overhead power line is at a height of $4\,m$ from the ground and carries a current of $100\,A$ from east to west. The magnetic field directly below it on the ground is $(\mu _0 = 4\pi \times 10^{-7}\,TmA^{-1})$

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

An electron revolves in a circle of radius $0.4 \text{ Å}$ with a speed of $10^6 \text{ m/s}$ in a hydrogen atom. The magnetic field produced at the centre of the orbit due to the motion of the electron (in Tesla) is: $\left[\mu_0 = 4\pi \times 10^{-7} \text{ H/m}, q = 1.6 \times 10^{-19} \text{ C}\right]$

The magnetic field induction produced at the centre of orbit due to an electron revolving in $n^{\text{th}}$ orbit of a hydrogen atom is proportional to