question_answer

A vertical wire of length t has its both ends fixed. Space around the wire has a horizontal magnetic field of strength B. If current; is passed through the wire such that its mid-point is deflected by amount x, tension in the wire is

A) \[\frac{Bi{{\ell }^{2}}}{x}\]

B) \[\frac{Bi{{\ell }^{2}}}{4x}\]

C) \[\frac{Bi{{x}^{2}}}{\ell }\]

D) \[\frac{Bi{{x}^{2}}}{4\ell }\]

Correct Answer: B

Solution :

Magnetic force on the wire

\[F=Bi\frac{\ell }{2}\sin \theta \simeq Bi\frac{\ell }{2}\tan \theta \]

\[=Bi\frac{\ell }{2}\times \frac{\ell /2}{x}\]

\[=\frac{Bi{{\ell }^{2}}}{4x}\]