MHTCET 16 Apr 2026 Shift 2 Paper

Concept:The magnetic field on the axis of a circular loop depends on the distance from the center, while the field at the center is the maximum value.Explanation:The magnetic field at the center of a circular loop of radius $R$ carrying current $I$ is given by:$$B_{\text{center}} = \frac{\mu_0 I}{2R}$$For a point on the axis at distance $x$ from the center, the magnetic field is:$$B_{\text{axis}} = \frac{\mu_0 I R^2}{2\left(R^2 + x^2\right)^{3/2}}$$Here, the point is at distance $R$ from the center, so substitute $x = R$:$$B_{\text{axis}} = \frac{\mu_0 I R^2}{2\left(R^2 + R^2\right)^{3/2}}$$$$B_{\text{axis}} = \frac{\mu_0 I R^2}{2\left(2R^2\right)^{3/2}}$$$$B_{\text{axis}} = \frac{\mu_0 I R^2}{2 \cdot 2^{3/2} R^3}$$$$B_{\text{axis}} = \frac{\mu_0 I}{2^{5/2} R}$$Now, take the ratio of the two fields:$$\frac{B_{\text{center}}}{B_{\text{axis}}} = \frac{\frac{\mu_0 I}{2R}}{\frac{\mu_0 I}{2^{5/2} R}}$$$$\frac{B_{\text{center}}}{B_{\text{axis}}} = \frac{2^{5/2}}{2} = 2^{3/2} = \sqrt{8}$$Answer:Therefore, $B_{\text{center}} : B_{\text{axis}} = \sqrt{8} : 1$, which matches option C.