A) \[\frac{2\pi rn}{q}\times {{10}^{-7}}\]
B) \[\left( \frac{2\pi q}{r} \right)\times {{10}^{-7}}\]
C) \[\left( \frac{2\pi q}{nr} \right)\times {{10}^{-7}}\]
D) \[\left( \frac{2\pi nq}{r} \right)\times {{10}^{-7}}\]
Correct Answer: D
Solution :
Magnetic field at the centre \[B=\frac{{{\mu }_{0}}nl}{2r}\] \[B=\frac{2{{\mu }_{0}}nl}{4r\pi }\times \pi \] \[B=\frac{2{{\mu }_{0}}n/\pi }{4\pi r}\] \[B=\frac{2\pi nl}{r}\times {{10}^{-7}}\] \[\left[ \because \,\frac{{{\mu }_{0}}}{4\pi }={{10}^{-7}} \right]\] \[B=\left( \frac{2\pi nq}{r} \right)\times {{10}^{-7}}\] \[[\because \,q=lt]\]
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