question_answer

Work done on an electron moving in a solenoid along its axis is equal to

A)  zero                     

B)  -evB

C)  ilB                         

D)  None of these

Correct Answer: A

Solution :

                A magnetic field is produced around and within the solenoid. The magnetic field within the solenoid is uniform and parallel to the axis of solenoid.                 \[{{F}_{m}}=q(\overrightarrow{\mathbf{v}}\times \overrightarrow{\mathbf{B}})=Bqv\,\,\sin \theta \] Since, angle between \[\overrightarrow{\mathbf{v}}\] and \[\overrightarrow{\mathbf{B}}={{0}^{o}}\], therefore \[{{F}_{m}}=0\]. Now,      \[W=\overrightarrow{\mathbf{F}}\,\times \overrightarrow{\mathbf{d}}\,\cos \,\phi \] Since       \[F=0\] \[\Rightarrow \]                               \[W=0\]