The magnetic induction at the centre $O$ of the current carrying bent wire shown in the adjoining figure is
$\frac{{{\mu _0}I}}{{4\pi {R_1}}}\alpha $
$\frac{{{\mu _0}I}}{{4\pi {R_2}}}\alpha $
$\frac{{{\mu _0}I\alpha }}{{4\pi }}\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$
$\frac{{{\mu _0}I\alpha }}{{4\pi }}\left( {\frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}} \right)$
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?
The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1=2 \pi\ \mathrm{m}$ and $R_2=4 \pi\ \mathrm{m}$ carrying current $I=4 \mathrm{~A}$ as per figure given below is $\alpha \times 10^{-7} \mathrm{~T}$. The value of $\alpha$ is___________ (Centre $\mathrm{O}$ is common for all segments)
A tightly wound $100$ turns coil of radius $10 \mathrm{~cm}$ carries a current of $7 \mathrm{~A}$. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 \pi \times 10^{-7} \mathrm{SI}$ units):
State scientists research about electricity and magnetism after Oersted’s observation.
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.