A) \[\frac{\sqrt{5}{{\mu }_{0}}I}{2R}\]
B) \[\frac{3{{\mu }_{0}}I}{2R}\]
C) \[\frac{{{\mu }_{0}}I}{2R}\]
D) \[\frac{{{\mu }_{0}}I}{R}\]
Correct Answer: A
Solution :
[a] The magnetic field, due the coil, carrying current \[I\]Ampere \[{{B}_{1}}=\frac{{{\mu }_{0}}I}{2R}\] The magnetic field due to the coil, carrying current I Ampere \[{{B}_{2}}=\frac{{{\mu }_{0}}(2I)}{2R}\] The resultant B \[{{B}_{net}}=\sqrt{B_{1}^{2}+B_{2}^{2}+2{{B}_{1}}{{B}_{2}}\,\cos \,\theta ,}\,\,\,\,\theta ={{90}^{o}}\] \[{{B}_{net}}=\sqrt{B_{1}^{2}+B_{2}^{2}}=\frac{{{\mu }_{0}}(2I)}{2R}\sqrt{1+4}=\frac{\sqrt{5}{{\mu }_{0}}I}{2R}\]You need to login to perform this action.
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