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  • The ratio of magnetic field at the centre of a current carrying coil of radius to the magnetic field at distance <img alt="r"

The ratio of magnetic field at the centre of a current carrying coil of radius r to the magnetic field at distance r from the centre of coil on its axis is \sqrt{\mathrm{x}}: 1.The value of \mathrm{x} is _____

Option: 1

8


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

B_{\text {axis }}=\frac{\mu_{0} i R^{2}}{2\left(R^{2}+x^{2}\right)^{3 / 2}}

\frac{\left(B_{\text {axis }}\right) x=R}{\left(B_{\text {axis }}\right) x=0}=\frac{\frac{\mu_{0} \mathrm{iR}^{2}}{2\left(R^{2}+R^{2}\right)^{3 / 2}}}{\frac{\mu_{0} i R^{2}}{2\left(R^{2}\right)^{3 / 2}}}=\frac{R^{3}}{2^{3 / 2} R^{3}}=\frac{1}{\sqrt{8}}

\frac{(B)_{A t_{\text {centrs }}}}{(B)_{A t} x=R}=\frac{\sqrt{8}}{1}

x=8

Posted by

Sumit Saini

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