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A proton of mass 1.67 xx 10^(-27) kg and...

A proton of mass `1.67 xx 10^(-27)` kg and charge `1.6 xx 10^(-19)` C is projected with a speed of `2 xx 10^(6)` m/s at an angle of `60^(@)` to the X–axis. If a uniform magnetic field of 0.104 tesla is applied along Y–axis, the path of proton is

A

A circle of radius = 0.2 m and time period `pi xx 10^(-7) s`

B

A circle of radius = 0.1 m and time period `2pi xx 10^(-7) s`

C

A helix of radius = 0.1 m and time period `2pi xx 10^(-7) s`

D

A helix of radius = 0.2 m and time period `4 pi xx 10^(-7) `s

Text Solution

Verified by Experts

The correct Answer is:
C
Since , `theta = 30^(@)` , path is helix
Radius ( r) = `(mv sin theta)/(q B)`
`implies r = (1.6 xx 10^(-27) xx 2 xx 10^(6) xx sin 30^(@))/(1.6 xx 10^(-19) xx 0.104)`
`= 0.1m`

Time (T) = `(2pi m)/(qB) = (2pi xx 1.67 xx 10^(-27))/(1.6 xx 10^(-19) xx 0.104)`
`= 2pi xx 10^(-7)` sec
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