A) \[\frac{2}{\sqrt{2}}{{\left( \frac{\tau }{Bi} \right)}^{1/2}}\]
B) \[\frac{2}{\sqrt{3}}\left( \frac{\tau }{Bi} \right)\]
C) \[2{{\left( \frac{\tau }{\sqrt{3}Bi} \right)}^{1/2}}\]
D) \[\frac{1}{\sqrt{3}}\frac{\tau }{Bi}\]
Correct Answer: C
Solution :
Torque acting on equilateral triangle in a magnetic field \[\overrightarrow{B}\] is \[\tau =i\,AB\sin \theta \] Area of triangle LMN \[A=\frac{\sqrt{3}}{4}{{l}^{2}}\] and \[\theta =90{}^\circ \] Substituting the given values in the expression for torque, we have \[\tau =i\times \frac{\sqrt{3}}{4}{{l}^{2}}B\sin 90{}^\circ \] \[=\frac{\sqrt{3}}{4}i\,{{l}^{2}}B\] \[(\because \sin 90{}^\circ =1)\] Hence, \[l=2{{\left( \frac{\tau }{\sqrt{3}Bi} \right)}^{1/2}}\]You need to login to perform this action.
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