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A particle of mass m and charge q has an...

A particle of mass m and charge q has an initial velocity `vecv =v_(0)hatj`. If an electric field `E = E_(0)hati` and `B = B_(0)hati` magnetic field act on the particle, its speed will double after a time

A

`t=(sqrt(3)mv_(0))/(qE)`

B

`t=(sqrt(2)mv_(0))/(qE)`

C

`t=(mv_(0))/(qE)`

D

`t=(mv_(0))/(2qE)`

Text Solution

Verified by Experts

The correct Answer is:
A

Magnitude of velocity doesn.t change in Y-Z plane.
`(2v_(0))^(2) =v_(0)^(2) +v_(x)^(2)`
`therefore v_(x) = sqrt(3)v_(0)`
`therefore` From equation of motion,
`v_(x) =v_(0x) + a_(0x)t`
`therefore sqrt(3)v_(0) =(qE)/mt, therefore t=(sqrt(3)mv_(0))/(qE)`
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