question_answer

An electron, moving in a uniform magnetic field of induction of intensity B, has its radius directly proportional to :

A)  its charge      

B)  magnetic field

C)  speed         

D)  none of these

Correct Answer: C

Solution :

 Key Idea: Force due to magnetic field provides the required centripetal force. The force due to magnetic field acting on the electron of mass m is \[F=ev\,\,B\] ?. (i) The centripetal force is given by \[F=\frac{m{{v}^{2}}}{r}\] ?. (ii) where r is radius of circular path. Equating Eq.(i) with Eq.(ii), weget \[F=qvB=\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \] \[r=\frac{mv}{qB}\] \[\Rightarrow \] \[r\propto v\]. Note: If the speed of the particle increases is radius also increases, so that time taken to complete one revolution remains same.