A closely packed coil having $1000$ turns has an average radius of $62.8\,cm$. If current carried by the wire of the coil is $1\,A$, the value of magnetic field produced at the centre of the coil will be (permeability of free space $=4 \pi \times 10^{-7}\,H / m$ ) nearly

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.

The magnetic field at the origin due to a current element $i\,\overrightarrow {dl} $ placed at position $\vec r$ is

$(i)\,\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$

$(ii)\,\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$

$(iii)\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$

$(iv)\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is $1: 1$. The magnetic field at point $P$ is ...... .

.......$A$ should be the current in a circular coil of radius $5\,cm$ to annul ${B_H} = 5 \times {10^{ - 5}}\,T$

Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r$ = radius of ring)