A) \[\frac{65\pi a{{R}^{4}}}{2592}\]
B) \[\frac{25\pi a{{R}^{4}}}{72}\]
C) \[\frac{65\pi {{a}^{2}}{{R}^{4}}}{2938}\]
D) \[\frac{81\pi {{a}^{2}}{{R}^{4}}}{144}\]
Correct Answer: A
Solution :
[a]: Current density \[J=a{{r}^{2}}\] Current \[I=\int_{{}}^{{}}{J.dA}=\int\limits_{R/3}^{R/2}{a{{r}^{2}}(2\pi rdr)}\] [where \[dA=2\pi dr\]] \[=2\pi a\left[ \frac{{{r}^{4}}}{4} \right]_{R/3}^{R/2}=\frac{65\pi a{{R}^{4}}}{2592}\]
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