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  • The magnetic field at the centre of a circular coil of radius , due to current <img alt="\mathrm{I}" s

The magnetic field at the centre of a circular coil of radius \mathrm{r}, due to current \mathrm{I} flowing through it, is \mathrm{B}. The magnetic field at a point along the axis at a distnace \mathrm{\frac{r}{2}} from the centre is :

Option: 1

\mathrm{B/2}


Option: 2

\mathrm{2B}


Option: 3

\mathrm{\left [ \frac{2}{\sqrt{5}} \right ]^{3}B}


Option: 4

\mathrm{\left [ \frac{2}{\sqrt{3}} \right ]^{3}B}


Answers (1)

best_answer

\mathrm{B= B_{circular \: coil}= \frac{\mu _{0}i}{2r}}
\mathrm{B^{\prime}= B_{axis}= \frac{\mu _{0}\, i\, r^{2}}{2\left ( r^{2}+x^{2} \right )^{3/2}}= \frac{\mu _{0}\, i\, r^{2}}{2\times\frac{ 5\sqrt{5}\, r^{3}}{8}}}
\mathrm{\frac{B}{B^{\prime}}= \frac{5\sqrt{5}}{8}}
\mathrm{B^{\prime}= \left ( \frac{2}{\sqrt{5}} \right )^{3}B}

The correct option is (3)

Posted by

Pankaj Sanodiya

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