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The magnetic field in a certain region o...

The magnetic field in a certain region of space is given by `B=8.35 xx10^(-2) hati T.`A proton is shot into the field with velocity `v=(2xx10^(5)hati+4xx10^(5)hatj)m//s.` the proton follows a helical path in the field. The distance moved by proton in the x-direction during the period of one revolution in the yz-plane will be ( mass of proton`=1.67 xx 10^(-27) kg)`

A

0.053 m

B

0.136 m

C

0.157 m

D

0.236 m

Text Solution

Verified by Experts

The correct Answer is:
C
`vecv = (2 xx 10^(5) hati + 4 xx 10^(5) hatj) m//s`
`vecB = 8.35 xx 10^(-2) hati T`
Pitch = `v_(i) T = (2pi m V_(1))/(qB) " "` [As `T = (2pi m)/(qB)]`
`= (2 xx 3.14 xx 1.67 xx 10^(-27) xx 2 xx 10^(5) )/(1.6 xx 10^(-19) xx 8.35 xx 10^(-2)) = 0.157` m
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