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Question

(D) The magnetic field $B$ on the axis of a circular loop of radius $R$ carrying current $I$ at a distance $x$ from the center is given by the formula

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$B = \frac{\mu_0 I}{4\sqrt{2}R}$

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(D) The magnetic field $B$ on the axis of a circular loop of radius $R$ carrying current $I$ at a distance $x$ from the center is given by the formula: $B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$.Given that the distance from the center is equal to the radius, we have $x = R$.Substituting $x = R$ into the formula:$B = \frac{\mu_0 I R^2}{2(R^2 + R^2)^{3/2}}$$B = \frac{\mu_0 I R^2}{2(2R^2)^{3/2}}$$B = \frac{\mu_0 I R^2}{2(2^{3/2} R^3)}$$B = \frac{\mu_0 I}{2 \cdot 2^{3/2} R}$$B = \frac{\mu_0 I}{2^{5/2} R}$ or $B = \frac{\mu_0 I}{4\sqrt{2} R}$.

Write the equation for the magnetic field on the axis of a circular current-carrying loop at a distance from the center equal to its radius.

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