A uniform conducting wire of length is \(24 {a}\), and resistance \({R}\) is wound up as a current carrying coil in the shape of an equilateral triangle of side \('a'\) and then in the form of a square of side \('a'.\) The coil is connected to a voltage source \({V}_{0}\). The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is \(1: \sqrt{y}\) where \(y\) is ..... .

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Answer & Solution

Correct Answer

(A) \(3\)

Detailed explanation

In triangle shape \({N}_{{t}}=\frac{24 {a}}{3 {a}}=8\)

In square \({N}_{{s}}=\frac{24 {a}}{4 {a}}=6\)

\(\frac{{M}_{{t}}}{{M}_{3}}=\frac{{N}_{{t}} {IA}_{{t}}}{{N}_{{s}} {I}_{{s}}}[{I}\) will be same in both \(]\)

\(=\frac{8 \times \frac{\sqrt{3}}{4} \times a^{2}}{6 \times a^{2}}\)

\(\frac{{M}_{{t}}}{{M}_{{s}}}=\frac{1}{\sqrt{3}}\)

\({y}=3\)

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