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

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

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

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

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

A closely wounded circular coil of radius $5\,cm$ produces a magnetic field of $37.68 \times 10^{-4}\,T$ at its center. The current through the coil is $......A$. [Given, number of turns in the coil is $100$ and $\pi=3.14]$

A circular coil of wire consisting of $100$ turns, each of radius $8.0\; cm$ carries a current of $0.40\, A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?

Field at the centre of a circular coil of radius $r$, through which a current $I$ flows is

An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has magnitude

A circular coil is in $y-z$ plane with centre at the origin. The coil is carrying a constant current. Assuming direction of magnetic field at $x = -25\, cm$ to be positive direction of magnetic field, which of the following graphs shows variation of magnetic field along $x-$ axis