A) \[\frac{{{\mu }_{0}}i}{2\sqrt{2}R}\]
B) \[\frac{{{\mu }_{0}}i}{2R}\]
C) \[\frac{{{\mu }_{0}}i}{4R}\]
D) \[\frac{{{\mu }_{0}}i}{\sqrt{2}R}\]
Correct Answer: A
Solution :
The magnetic field at centre O for each semicircular parts each of radius R, \[{{B}_{1}}={{B}_{2}}=\frac{{{\mu }_{0}}i}{4R}\] The magnetic field at their common centre \[\overset{\to }{\mathop{\mathbf{B}}}\,=\overset{\to }{\mathop{{{\mathbf{B}}_{1}}}}\,+\overset{\to }{\mathop{{{\mathbf{B}}_{2}}}}\,\] \[B=\sqrt{B_{1}^{2}+B_{2}^{2}}\] \[=\sqrt{{{\left( \frac{{{\mu }_{0}}i}{4R} \right)}^{2}}+{{\left( \frac{{{\mu }_{0}}i}{4R} \right)}^{2}}}\] \[B=\frac{{{\mu }_{0}}i}{2\sqrt{2}R}\]
You need to login to perform this action.
You will be redirected in
3 sec
