Question
Mon April 20, 2015 By: Kb Aulakh

An electron is moving on a circular orbit of radius r with speed v.It produces a magnetic feild B at its centre,then radius of circle is proprortional to;
Options:
1.v/B
2.v/Bsquare
3.[v/B]square
4.[v/B]raised to power half
 

Expert Reply
Jyothi Nair
Tue April 21, 2015
As the electron is moving perpendicular to the direction of magnetic field, it experiences a maximum force which acts perpendicular to the direction of magnetic field as well as begin mathsize 12px style straight v with rightwards arrow on top end style . 
This force will provide the required centripetal force for the electron to describe a circular path in the magnetic field of radius r:
Hence we can write that:
 
begin mathsize 14px style mv squared over straight r equals straight B space straight q space straight v mv over straight r equals straight B space straight q rightwards double arrow straight r space equals space fraction numerator straight m space straight v over denominator straight B space straight q end fraction straight i. straight e. space straight r space equals straight m over straight q cross times straight v over straight B For space an space electron space straight m over straight q space is space space straight a space constant comma space hence space we space get space that colon Radius space of space the space circle comma space straight r space straight alpha space straight v over straight B end style
 
Therefore the correct option is 1. v / B

i.e Radius of the circle is proprortional to v / B
Home Work Help