The magnetic field intensity at the point $O$ of a loop with current $i$, whose shape is illustrated below is
$\frac{\mu_0 i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}\right]$
$\frac{\mu_0 i}{4 \pi^2}\left[\frac{2}{a}+b\right]$
$\frac{\mu_0 i}{2 \pi}\left[\frac{1}{a}+\frac{1}{b}\right]$
$\frac{\mu_0 i}{4 \pi}\left[\frac{1}{a}+\frac{1}{b}\right]$
A long conducting wire having a current $I$ flowing through it, is bent into a circular coil of $N$ turns.Then it is bent into a circular coil of $n$ tums. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:
$A$ and $B$ are two concentric circular conductors of centre $O$ and carrying currents ${i_1}$ and ${i_2}$ as shown in the adjacent figure. If ratio of their radii is $1 : 2$ and ratio of the flux densities at $O$ due to $A$ and $B$ is $1 : 3$, then the value of ${i_1}/{i_2}$ is
Two long straight wires are placed along $x$-axis and $y$-axis. They carry current $I_1$ and $I_2$ respectively. The equation of locus of zero magnetic induction in the magnetic field produced by them is
Current through $ABC$ and $A'B'C'$ is $I$. What is the magentic field at $P$ ? $BP = PB' = r$ (Here $C'B'PBC$ are collinear)
A current carrying loop consists of $3$ identical quarter circles of radius $\mathrm{R}$, lying in the positive quadrants of the $\mathrm{xy}$ , $\mathrm{yz}$ and $\mathrm{zx}$ planes with their centres at the origin, joined together. Find the direction and magnitude of $\mathrm{B}$ at the origin.