The magnetic field at the centre of a current | vedclass

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(C) The magnetic field at the centre of a circular loop is given by $B_{center} = \frac{\mu_0 I}{2R} = 16 \ \mu T$.The magnetic field at a distance $x

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$2$

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(C) The magnetic field at the centre of a circular loop is given by $B_{center} = \frac{\mu_0 I}{2R} = 16 \ \mu T$.The magnetic field at a distance $x$ on the axis of the loop is given by $B_{axis} = \frac{\mu_0 I R^2}{2(x^2 + R^2)^{3/2}}$.Given $x = \sqrt{3}R$, we substitute this into the formula:$B_{axis} = \frac{\mu_0 I R^2}{2((\sqrt{3}R)^2 + R^2)^{3/2}} = \frac{\mu_0 I R^2}{2(3R^2 + R^2)^{3/2}} = \frac{\mu_0 I R^2}{2(4R^2)^{3/2}}$.Simplifying the denominator:$(4R^2)^{3/2} = (2R)^3 = 8R^3$.Thus, $B_{axis} = \frac{\mu_0 I R^2}{2 	imes 8R^3} = \frac{1}{8} 	imes \left(\frac{\mu_0 I}{2R}ight)$.Substituting $B_{center} = 16 \ \mu T$:$B_{axis} = \frac{1}{8} 	imes 16 \ \mu T = 2 \ \mu T$.

The magnetic field at the centre of a current-carrying circular loop of radius $R$ is $16 \ \mu T$. The magnetic field at a distance $x = \sqrt{3}R$ on its axis from the centre is . . . . . . $\mu T$.

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