In the current-carrying conductor $(AOCDEFG)$ as shown,the magnetic induction at the point $O$ is ($R_1$ and $R_2$ are radii of arcs $CD$ and $EF$ respectively,$I$ = current in the loop,$\mu_0$ = permeability of free space).

$A$ circular loop and an infinitely long straight conductor carry equal currents,as shown in the figure. The net magnetic field at the centre of the loop is $B_1$,when the current in the loop is clockwise and $B_2$ when the current in the loop is anti-clockwise. Then $\frac{B_1}{B_2}$ is

$A$ 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

What is the magnetic field at point $P$ in the given figure?

The magnetic field at the origin due to a current element $i \, d\vec{l}$ placed at position $\vec{r}$ is given by the Biot-Savart Law. Which of the following expressions correctly represent this magnetic field?
$(i) \, \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{d\vec{l} \times \vec{r}}{r^3} \right)$
$(ii) \, - \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{d\vec{l} \times \vec{r}}{r^3} \right)$
$(iii) \, \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{\vec{r} \times d\vec{l}}{r^3} \right)$
$(iv) \, - \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{\vec{r} \times d\vec{l}}{r^3} \right)$

Two long parallel wires are at a distance $R$ apart. They carry steady equal currents in the same directions as shown in the figure. The ratio of magnetic fields at $A, B$ and $C$ respectively,is