A) double of its first value
B) quarter of its first value
C) four times of its first value
D) same as the first value
Correct Answer: A
Solution :
For first case the wire of length L is bent to form a circular coil of one turn, \[\operatorname{L}=2\pi {{r}_{1}}\] Similarly, for second case \[\operatorname{L} = 4\pi {{r}_{2}}\] Now, \[2\pi {{r}_{1}}= 4\pi {{r}_{2}}\,\,\Rightarrow \,\,{{r}_{2}}=\frac{{{r}_{1}}}{2}\] \[{{B}_{1}}=\frac{{{\mu }_{0}}l}{2{{r}_{1}}}\,\,\,and\,\,\,\,\,{{B}_{2}}=\frac{{{\mu }_{0}}l}{2{{r}_{2}}}={{\left( \frac{{{\mu }_{0}}l}{2{{r}_{1}}} \right)}^{2}}\] \[{{B}_{2}}=2{{B}_{1}}\]
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