$A$ current $I$ flows in a wire bent in the shape of a quarter ring of radius $R$ as shown in the figure. The magnetic field induction $B$ at point $O$ is

State the Biot-Savart law.

The magnetic field at the origin due to a current element $i d l$ placed at a point with vector position $r$ is

Two long parallel wires are separated by a distance of $2.50 \ cm$. The force per unit length that each wire exerts on the other is $4 \times 10^{-5} \ N \ m^{-1}$, and the wires repel each other. The current in one wire is $0.5 \ A$. What is the current in the second wire (in $A$)? (Take $\mu_0 = 4 \pi \times 10^{-7} \ S.I. \ \text{unit}$)

$A$ thin charged rod is bent into the shape of a small circle of radius $R$, the charge per unit length of the rod being $\lambda$. The circle is rotated about its axis with a time period $T$, and it is found that the magnetic field at a distance $d$ away $(d >> R)$ from the center and on the axis varies as $\frac{R^{m}}{d^{n}}$. The values of $m$ and $n$ respectively are:

$A$ steady current is set up in a cubic network composed of wires of equal resistance and length $d$ as shown in the figure. What is the magnetic field at the centre $P$ due to the cubic network?