Question

An electron is projected with velocity v0 in a uniform electric field E perpendicular to the field. Again it is projected with velocity v0 perpendicular to a uniform magnetic field B. If r1 is initial radius of curvature just after entering in the electric field and r2 is initial radius of curvature just after entering in magnetic field then the ratio r1/r2 is equal to :

A
Bv20E
B
BE
C
Ev0B
D
Bv0E
Solution
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For electric field,

Refer image 1.

q change of electron.

Four due to electric field =qE

mv02Re=qE

where Re is radius of curvature,

1Re=qEmv02

=mv02qE=r1

In magnetic field,

Focus on electron =qV0B

Refer image 2.

Balancing of centripetal and centrifugal focuses,

mV02Rb=qV0B

Rb=mV0qB=r2

r1r2=RcRb=mV02qEmV0qB

r1r2=BV0E

Answer is option D

1461632_42321_ans_135b65982399495b95e9869e41a0e456.png

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