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 B 2 . The value

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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 B 2 . The value of B 1 B 2 will be

TestHub · Accepted Answer

Magnetic field at the centre of the loop i.e. $B_{1} = \frac{μ_{0} i}{2 R}$
Magnetic field on the axis of the loop is,
$B_{2} = \frac{μ_{0} i R^{2}}{2 {(R^{2} + x^{2})}^{\frac{3}{2}}} = \frac{μ_{0} i \times R^{2}}{2 {(R^{2} + 3 R^{2})}^{\frac{3}{2}}}$ $= \frac{μ_{0} i \times R^{2}}{2 \times 8 R^{3}}$ $= \frac{μ_{0} i}{2 \times 8 R}$
Therefore, the ratio $\frac{B_{1}}{B_{2}} = \frac{8}{1}$

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