A) \[\sqrt{3}R\]
B) \[\frac{R}{\sqrt{3}}\]
C) \[\left( \frac{2}{\sqrt{3}} \right)R\]
D) \[\frac{R}{2\sqrt{3}}\]
Correct Answer: A
Solution :
The magnetic field at the axis of a current carrying coil of radius R, and at a distance\[x\] from the centre of the coil is \[B=\frac{{{\mu }_{0}}}{4\pi }.\frac{2\pi i{{R}^{2}}}{{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\] Given, \[B={{B}_{centre}}\times \frac{1}{8}\] \[\Rightarrow \] \[\frac{{{\mu }_{0}}}{4\pi }\times \frac{2\pi i{{R}^{2}}}{{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}=8{{R}^{3}}\] \[\Rightarrow \] \[{{({{R}^{2}}+{{x}^{2}})}^{3/2}}=8{{R}^{3}}\] \[\Rightarrow \] \[x=\sqrt{3}R\]You need to login to perform this action.
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