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  • A wire carries a current. Maintaining the same current it is bent first to form a circular plane coil of one turn which produces a magnetic field B at the centre of the coil. The same length i

A wire carries a current. Maintaining the same current it is bent first to form a circular plane coil of one turn which produces a magnetic field B at the centre of the coil. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre of the double loop, caused by the same current in -

Option: 1

2B


Option: 2

\frac{B}{4}


Option: 3

4B


Option: 4

\frac{B}{2}


Answers (1)

best_answer

Let I be the current and l be the length of the wire

for\ 1 st\ case: B=\frac{\mu_0 I n}{2 r}=\frac{\mu_0 I \cdot \pi}{l}\\ for\ 2nd\ case: l=2\left(2 \pi r^{\prime}\right) \Rightarrow r^{\prime}=\frac{l}{4 \pi}\\ B^{\prime}=\frac{\mu_0 N 1}{2 r}=\frac{\mu_{02} I}{2 \frac{l}{4 \pi}}=\frac{4 \mu_0 I \pi}{l}=4 B

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vinayak

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