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`).
.

Options

A. Current sensitivity of galvanometer is 20 mA/division.
B. 2.25 cm
C. 1.22 cm
D. 1

Answer

D

Explanation

`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^(-2))~~2.25cm`
`sin theta=(2cm)/R=(2xx4)/9, sin =8/9, y=6 tan theta= 6xx8/(sqrt(17))~~12 cm`
So `d~~12.87cm{d=y+Delta}`