The magnetic field at the centre of a current carrying circular loop of radius R is 16 μ ~T . The magnetic field at a distance x= 3 R on its axis from the centre is \_\_\_\_ μ T .

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Correct answer: B. 2

The magnetic field at the center of a circular loop is

B_{center} = \frac{\mu_0 I}{2R} = 16\mu

T.
On the axis at distance

x

from center:

B(x) = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}

.
At

x = \sqrt{3}R

:

B(\sqrt{3}R) = \frac{\mu_0 I R^2}{2(R^2 + 3R^2)^{3/2}} = \frac{\mu_0 I R^2}{2(4R^2)^{3/2}} = \frac{\mu_0 I}{16R}

.
The ratio:

\frac{B(\sqrt{3}R)}{B_{center}} = \frac{1/16R}{1/2R} = \frac{1}{8}

.
Therefore:

B(\sqrt{3}R) = \frac{1}{8} \times 16\mu = 2\mu

T.

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