A) \[\frac{{{\mu }_{0}}i({{r}_{1}}+{{r}_{2}})}{4}\]
B) \[\frac{{{\mu }_{0}}i({{r}_{1}}-{{r}_{2}})}{4}\]
C) \[\frac{{{\mu }_{0}}i({{r}_{1}}+{{r}_{2}})}{4{{r}_{1}}{{r}_{2}}}\]
D) \[\frac{{{\mu }_{0}}i({{r}_{2}}-{{r}_{1}})}{4{{r}_{1}}{{r}_{2}}}\]
Correct Answer: C
Solution :
In the given circuit, current in the upper and lower segments are in the opposite directions. Hence, magnetic field induction due to current through both the semicircles will be in the downward direction, therefore \[B={{B}_{1}}+{{B}_{2}}\] \[=\frac{{{\mu }_{0}}i}{4{{r}_{1}}}+\frac{{{\mu }_{0}}i}{4{{r}_{2}}}=\frac{{{\mu }_{0}}i}{4{{r}_{1}}{{r}_{2}}}({{r}_{1}}+{{r}_{2}})\]
You need to login to perform this action.
You will be redirected in
3 sec
