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An electron moving along the x-axis with...

An electron moving along the x-axis with an initial energy of `100 eV` enters a region of magnetic field `vec(B) = (1.5 xx 10^(-3) T) hat (k)` at `S` (see figure). The field extends between `x=0` and `x=2 cm`. The electron is detected at the point `Q` on a screen placed `8` cm away from the point `S`. The distance `d` between `P` and `Q` (on the screen) is :
(electron's charge `= 1.6 xx 10^(-19) C`, mass of electron `= 9.1 xx 10^(-31) kg`).
.

A

11.65 cm

B

2.25 cm

C

1.22 cm

D

12.87 cm

Text Solution

Verified by Experts

The correct Answer is:
D

`R=(sqrt(2mxx100eV))/(eB)=sqrt((2xx9.1xx10^(-31)xx6.6xx10^(-17))/(1.6xx10^(-19)xx1.5xx10^(-3)))`
`=(sqrt(29.12)10^(-24))/(1.6xx1.5xx10^(-22))~~2.25cm`
`sin theta=(2cm)/R=(2xx4)/9, sin=8/9`
`y=6 tan theta=6xx8//(sqrt(17))~~12 cm`
So `d~~12.87xcm{d=y+Delta}`
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