A) \[{{\mu }_{0}}\pi {{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
B) \[2{{\mu }_{0}}\pi {{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
C) \[\left( \frac{{{\mu }_{0}}}{4\pi } \right){{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
D) \[\left( \frac{{{\mu }_{0}}}{2\pi } \right){{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
Correct Answer: A
Solution :
[a] Current, \[I=\frac{2\pi r\sigma }{\ell /n}=2\pi r\sigma n\]. \[B=\frac{{{\mu }_{0}}I{{r}^{2}}}{2{{({{y}^{2}}+{{r}^{2}})}^{3/2}}}=\frac{{{\mu }_{0}}I{{r}^{2}}}{2{{y}^{3}}}\] If \[y>>r\]. \[B=\frac{{{\mu }_{0}}{{r}^{2}}}{2{{y}^{2}}}(2\pi r\sigma n)=\frac{{{\mu }_{0}}\pi {{r}^{3}}\sigma n}{{{y}^{3}}}\]
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