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Question

Two circular coils X and Y, having equal number of turns and carrying currents in the same sense, subtend same solid angle at point O. If the smaller coil X is midway between O and Y and if we represent the magnetic induction due to bigger coil Y at O as B_{y} and that due to smaller coil Y at O as B_{x}, then find the ratio B_{x}/B_{y}.

Moderate

Solution

${B}_{y}=\frac{{\mu}_{0}}{4\pi}\frac{2\pi I(2r{)}^{2}}{{\left[(2r{)}^{2}+(2d{)}^{2}\right]}^{3/2}},{B}_{x}=\frac{{\mu}_{0}}{4\pi}\frac{2\pi I{r}^{2}}{{\left[{r}^{2}+{d}^{2}\right]}^{3/2}}\phantom{\rule{0ex}{0ex}}\text{solve to get}\frac{{B}_{x}}{{B}_{y}}=2$

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