Magnetic Effects & Magnetism

JEE Main level, single correct, medium

31 of 276

Question 31 of 276

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at a2\frac{a}{2} and 2a2 a from axis of the wire is :

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Answer: (B) 1:11: 1

B12πa2=μoI4 B1=μoI4πaB22π2a=μoIB2=μoI4πa\begin{aligned} & \mathrm{B}_1 2 \pi \frac{\mathrm{a}}{2}=\mu_{\mathrm{o}} \frac{\mathrm{I}}{4} \\ & \mathrm{~B}_1=\frac{\mu_{\mathrm{o}} \mathrm{I}}{4 \pi \mathrm{a}} \\ & \mathrm{B}_2 2 \pi 2 \mathrm{a}=\mu_{\mathrm{o}} \mathrm{I} \\ & \mathrm{B}_2=\frac{\mu_{\mathrm{o}} \mathrm{I}}{4 \pi \mathrm{a}}\end{aligned}

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