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  • A current i is flowing in a straight conductor of length L. The magnetic induction at a point on its axis at a distance <img alt="\frac{L}{4}" src="https://entrancecorner.oncodecogs.com/gif.la

A current i is flowing in a straight conductor of length L. The magnetic induction at a point on its axis at a distance \frac{L}{4} from its centre will be : 

Option: 1

Zero 


Option: 2

\frac{\mu _{0}i}{2\pi L}


Option: 3

\frac{\mu _{0}i}{\sqrt{2} L}

 


Option: 4

\frac{4\mu _{0}i}{\sqrt{5}\pi L}


Answers (1)

best_answer

 

\begin{array}{l} B=\frac{\mu_{0} i}{4 \pi R}\left(\sin \phi_{1}+\sin \phi_{2}\right) \\ \sin \phi_{1}=\sin \phi_{2}=\frac{L / 2}{\sqrt{(L / 2)^{2}+(L / 4)^{2}}}=\frac{1}{2(\sqrt{1 / 4+1 / 16})}=\frac{4}{2 \sqrt{5}} \\ \Rightarrow B=\frac{\mu_{0} i}{4 \pi R}\left(\frac{2 \times 4}{2 \sqrt{5}}\right) B=\frac{4 \mu_{0} i}{\sqrt{5} \pi R} \end{array}

Here R = L

So,

B =     \frac{4\mu _{0}i}{\sqrt{5}\pi L}

Posted by

sudhir.kumar

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