Moving Charges and Magnetism - Result Question 43
44. 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
[2002]
(a) $4 B$
(b) $B / 4$
(c) $B / 2$
(d) $2 B$
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Answer:
Correct Answer: 44. (a)
Solution:
- (a) Let $I$ be current and $l$ be the length of the wire.
For Ist case : $B=\frac{\mu_0 I n}{2 r}=\frac{\mu_0 I \times \pi}{l}$
where $2 \pi r=l$ and $n=1$
For IInd Case $: l=2(2 \pi r^{\prime}) \Rightarrow r^{\prime}=\frac{l}{4 \pi}$
$B^{\prime}=\frac{\mu_0 n I}{2 r^{\prime}}=\frac{\mu_0 2 I}{2 \frac{l}{4 \pi}}=\frac{4 \mu_0 I \pi}{l}=4 B$
