A thin circular frame of radius $'a'$ is made of insulating material. A square loop is constructed with in it. If loop carrying current $I$ , then magnetic induction at geometrical centre $'O'$ will be
$\frac{{2{\mu _0}I}}{{\pi a}}$
$\frac{{\sqrt 3 {\mu _0}I}}{{2\pi a}}$
$\frac{{2\sqrt 2 {\mu _0}I}}{{\pi a}}$
$\frac{{3\sqrt 3 {\mu _0}I}}{{2\pi a}}$
The magnetic field $d\overrightarrow B $ due to a small current element $d\overrightarrow {l\,} $ at a distance $\overrightarrow {r\,} $ and element carrying current $i$ is
The radius of a circular current carrying coil is $R$. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be $\frac{1}{2 \sqrt{2}}$ times that at the centre?
A thin ring of $10\, cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\,\pi \,rad\,{s^{ - 1}}$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8 \times {10^{ - 9}}\,T$, then the charge carried by the ring is close to $\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,N/{A^2}} \right)$
One of the two identical conducing wires of length $L$ is bent in the form of a circular loop and the other one into a circular coil of $N$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $(B_L)$ to that at the centre of the coil $(B_C),$; $.\,\frac {B_L}{B_C}$ will be
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