Question

Passage type questions :
A charged particle of mass ‘m' and charge ‘q’ is allowed to enter in a region of space in which uniform
electric and magnetic field can be created. The subsequent path of the particle in the region will depend
upon intial value of velocity and direction of the field.
10. If Ē=0,B=Bk and ī=vi+voj the path of the particle is
2tmv.
a) circle of radius in xy plane
b) helical with uniform pitch
Вq
Ba
[ ]
mvo
c) a circle of radius
V2mv,
Bq
in xy plane
d) helical with non uniform pitch​

Answer 1

Answer:

The force on a charge q of mass m moving with a velocity v in a magnetic field perpendicularly is given by ,

F

B

=qvB ,

electric force on charge q by a field is given by ,

F

E

=qE ,

as net force on charge q is zero therefore both the fields should be equal and opposite ,

F

B

=F

E

,

or qvB=qE ,

or v=E/B ,

radius of the circular pah is ,

r=mv/qB=m(E/B)/qB ,

now electric field is reduced by a factor of 2 , therefore

v

′

=E/2B ,

and r

′

=m(E/2B)/qB=(1/2)mE/qB

2

=r/2 ,

the particle moves in a circle of half the radius .