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
Verified by Toppr

#### For electric field,Refer image 1.q→ change of electron.Four due to electric field =qE∴mv02Re=qEwhere Re is radius of curvature,∴1Re=qEmv02∴=mv02qE=r1In magnetic field,Focus on electron =qV0BRefer image 2.Balancing of centripetal and centrifugal focuses,mV02Rb=qV0B ∴Rb=mV0qB=r2∴r1r2=RcRb=mV02qEmV0qB∴r1r2=BV0EAnswer is option D

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