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A particle of specific charge (q//m) is...

A particle of specific charge `(q//m)` is projected from the origin of coordinate with initial velocity `[ui-vj]` unifrom electric magnetic fields exist in the region along the +ydirection, of magnitude `E` and `B` The particle will definitely return to the origin once if .

A

`[vB//2piE]` is an integer

B

`(u^(2)+v^(2))^(1//2)[B//piE]` is an integer

C

`[vB//piE]` in an integer

D

`[uB//piE]` is an integer .

Text Solution

Verified by Experts

The correct Answer is:
C
Taking motion along y axis (con by electric field)
`alpha = y_(0) + u_(y)t + (1)/(2) q_(y) t^(2)`
` 0 = 0 - vt + (1)/(2) (qE)/(m) t^(2)`
`t = (2mv)/(qE)`
In this time charge must complex one oe more revolution in x -z plane due to magnetic field
`T = (2 pim)/(qB) = - 2 implies t = nt...(2)`
`2mv)/(qE) = nxx (2pim)/(qB) implies (vB)/(piE) ` .
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