A) \[\frac{{{\mu }_{0}}I}{2r}\]
B) \[\frac{\mu \,I\,{{r}^{2}}}{2\pi {{R}^{2}}}\]
C) \[\frac{\mu \,I}{2\pi r}\]
D) \[\frac{{{\mu }_{0}}I\,r}{2\pi {{R}^{2}}}\]
Correct Answer: D
Solution :
Let I' be the current in region \[r<R\] Then, \[I'=\frac{I}{\pi {{R}^{2}}}\pi \left( {{r}^{2}} \right)\] or \[\frac{I{{r}^{2}}}{{{R}^{2}}}\] So, magnetic field, \[B=\frac{{{\mu }_{0}}I'}{2\pi r}=\frac{{{\mu }_{0}}I{{r}^{2}}}{2\pi {{R}^{2}}r}=\frac{{{\mu }_{0}}Ir}{2\pi {{R}^{2}}}\]
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