A) \[\sqrt{3}R\]
B) \[R/\sqrt{3}\]
C) \[\left( \frac{2}{\sqrt{3}} \right)R\]
D) \[\frac{R}{2\sqrt{3}}\]
Correct Answer: A
Solution :
For a circular coil of radius a carrying a current \[i\], the magnetic field at point\[P\], distance\[x\]from coil is given by \[B=\frac{{{\mu }_{0}}i\,\,{{a}^{2}}}{2{{({{a}^{2}}+{{x}^{2}})}^{3/2}}}N{{A}^{-1}}{{m}^{-1}}\] ? (i) At the centre of coil\[x=0\] \[\therefore \] \[B=\frac{{{\mu }_{0}}i}{2a}N{{A}^{-1}}{{m}^{-1}}\] ? (ii) Given, \[B=\frac{1}{8}B\] \[\therefore \] \[\frac{{{\mu }_{0}}i\,\,{{a}^{2}}}{2{{({{a}^{2}}+{{x}^{2}})}^{3/2}}}=\frac{1}{8}\left( \frac{{{\mu }_{0}}i}{2a} \right)\] \[\Rightarrow \] \[\frac{{{a}^{2}}}{{{({{a}^{2}}+{{x}^{2}})}^{3/2}}}=\frac{1}{8a}\] \[\Rightarrow \] \[8\,\,{{a}^{3}}={{({{a}^{2}}+{{x}^{2}})}^{3/2}}\] \[\Rightarrow \]\[{{a}^{2}}+{{x}^{2}}=4{{a}^{2}}\] \[\Rightarrow \] \[x=\sqrt{3\cdot a}\] Given, \[a=R\] \[x=\sqrt{3}\,\,R\]You need to login to perform this action.
You will be redirected in
3 sec