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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 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 is

Option: 1

4B


Option: 2

B / 4


Option: 3

B / 2


Option: 4

2 B


Answers (1)

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Let I be current and l be the length of the wire. For Ist case :\mathrm{B}=\frac{\mu_0 \mathrm{In}}{2 \mathrm{r}}=\frac{\mu_0 \mathrm{I} \times \pi}{\mathrm{l}}where    2 \pi \mathrm{r}=\mathrm{l} and n=1 For IInd Case

: l=2\left(2 \pi r^{\prime}\right) \Rightarrow r^{\prime}=\frac{l}{4 \pi}

\mathrm{B}^{\prime}=\frac{\mu_0 \mathrm{nI}}{2 \mathrm{r}^{\prime}}=\frac{\mu_0 2 \mathrm{I}}{2 \frac{\mathrm{l}}{4 \pi}}=\frac{4 \mu_0 \mathrm{I} \pi}{\mathrm{l}}=4 \mathrm{~B}

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