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

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

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

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

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

Question

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

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

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

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

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

Medium

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Solution

Vector form of Bio-savart law but need to calculate at origin.

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