A) \[\frac{2\pi {{B}_{0}}{{r}^{3}}}{5{{\mu }_{0}}}\]
B) \[\frac{\pi {{B}_{0}}{{r}^{4}}}{2{{\mu }_{0}}}\]
C) \[\frac{2\pi {{B}_{0}}{{r}^{2}}}{{{\mu }_{0}}}\]
D) \[\frac{2\pi {{B}_{0}}{{r}^{4}}}{{{\mu }_{0}}}\]
Correct Answer: D
Solution :
[d] \[\oint{Bd\ell ={{\mu }_{0}}{{I}_{en}}}\] \[\oint{{{B}_{0}}{{r}^{3}}d\ell ={{\mu }_{0}}{{I}_{en}}}\] or \[{{B}_{0}}{{r}^{3}}\int\limits_{0}^{2gpr}{d\ell ={{\mu }_{0}}{{I}_{en}}}\] [Note: \[{{B}_{0}}{{r}^{3}}\] is taken out of integration because it is not varying along \[d\,\ell \] .] or \[{{B}_{0}}{{r}^{3}}(2\pi r)={{\mu }_{0}}{{I}_{en}}\] or \[{{I}_{en}}=\frac{2\pi {{B}_{0}}{{r}^{4}}}{{{\mu }_{0}}}\]You need to login to perform this action.
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