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  4. The magnetic field at the center of current carrying circular loop is B 1. The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B2. The value of B1 / B2 will be

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Q. The magnetic field at the center of current carrying circular loop is $B _1$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_2$. The value of $B_1 / B_2$ will be

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Solution:

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$ B _1=\frac{\mu_0 I }{2 R } $
$B _2=\frac{\mu_0 IR ^2}{2\left( R ^2+3 R ^2\right)^{3 / 2}}=\frac{1}{8}\left(\frac{\mu_0 I }{2 R }\right)=\frac{ B _1}{8} $
$ \frac{ B _1}{ B _2}=\frac{8}{1}$