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  4. The magnetic fields at two points on the axis of a circular coil at distance of 0.05 m and 0.2 m from the centre are in the ratio 8 :1 . The radius of the coil is

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Q. The magnetic fields at two points on the axis of a circular coil at distance of 0.05 m and 0.2 m from the centre are in the ratio 8 :1 . The radius of the coil is

KCETKCET 2001

Solution:

$\frac{B_1}{B_2} \frac{(r^2 + x_2^2)^{3/2}}{(r^2 + x_1^2)^{3/2}} \, i.e. \frac{8}{1} = \frac{(r^2 + 20^2)^{3/2}}{(r^2 + 5^2)^{3/2}} \, i.e. \, r $ = 0.1 m