A) \[\frac{1}{2}\]
B) \[\frac{3}{2}\]
C) \[2\]
D) \[\frac{2}{3}\]
Correct Answer: D
Solution :
[d] \[B=\frac{\left( {{\mu }_{0}} \right)I}{2\pi r}=\frac{\left( {{\mu }_{0}} \right)\left( J \right)\pi {{r}^{2}}}{2\pi r}=\frac{{{\mu }_{0}}Jr}{2}\] \[{{B}_{1}}\left( at\frac{a}{3} \right)=\frac{{{\mu }_{0}}Ja}{6}\] \[{{B}_{2}}\left( at\,2a \right)=\frac{\left( {{\mu }_{0}} \right)\left( J \right)\pi {{a}^{2}}}{2\pi \left( 2a \right)}=\frac{{{\mu }_{0}}Ja}{4}\] \[\Rightarrow \frac{{{B}_{1}}}{{{B}_{2}}}=\frac{2}{3}\]
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