The magnetic field in a certain region of space is given by ` vec B = 8.35 xx 10^(-2)` T. A proton is shot into the field with velocity `vec v = ( 2 xx 10^5 hat i + 4 xx 10^5 hat j)` 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 jz-plane will be (Mass of proton `= 1.67 xx 10^(-27) kg)`

Options

A. 0.053m
B. 0.136m
C. 0.157m
D. 0.236m

Answer

C

Explanation

Here `vec B = 0.35 xx 10^(-2) hat i T`
`vec v = 2 xx 10^5 hat` i Pitch of the helix (i.e, the liner distance mooved along moved along the magnified field in one rotation) is given by
Pitch of the helix `=(2pim_(||))/(qb)`
`=(2xx3.14xx1.67xx10^(-7)xx2xx10^(5))/(1.6xx10^(-19)xx8.35xx10^(-2))=0.157m`