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

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

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

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

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

Find the magnitude of magnetic field at point $p$ due to a semi - infinite wire given below

A Rowland ring of mean radius $15\; cm\;3500$ turns of wire wound on a ferromagnetic core of relative permeability $800.$ What is the magnetic field $B$ (in $T$) in the core for a magnetizing current of $1.2\; A?$

Two identical coils of radius $R$ and number of turns $N$ are placed perpendicular to each others in such a way that they have common centre. The current through them are $I$ and $I\sqrt 3$ . The resultant intensity of magnetic field at the centre of the coil will be  (in $weber/m^2)2$

The magnetic field intensity at the point $O$ of a loop with current $i$, whose shape is illustrated below is

A uniform wire is bent in the form of a circle of radius $R$. A current $I$ enters at $A$ and leaves at $C$ as shown in the figure :If the length $ABC$ is half of the length $ADC,$ the magnetic field at the centre $O$ will be