The ratio of the magnetic field at the centre of a current carrying coil of the radius $a$ and at a distance ‘$a$’ from centre of the coil and perpendicular to the axis of coil is
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(d) $\frac{{{B_c}}}{{{B_a}}} = {\left( {1 + \frac{{{x^2}}}{{{a^2}}}} \right)^{3/2}} = {\left( {1 + \frac{{{a^2}}}{{{a^2}}}} \right)^{3/2}} = {\left( {1 + 1} \right)^{3/2}} = 2\sqrt 2 $
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