Question

A stream of electrons moving with a velocity of 3 x 107ms-1is deflected by 2mm in traversing a distance of 0.1m in a uniform electric field of strength 18Vcm-1. Determine e / m of electrons.

Answer 1

Let electron moves along x axis with constant velocity v, due to present of electric along y axis, electron deflected from its path.

Let t is time taken to travel x distance with speed v m/s by electron .

so, x = vt

=> t = x/v

= 0.1/(3 × 10^7)

= 10/3 × 10^-9sec

now, deflection of electron in y axis :

y = 1/2 at²

or, 2mm = 1/2 × a × t²

using, F = ma = qE

or, a = qE/m = eE/m

so, 2mm = 1/2 × (eE/m)t²

or, 2 × 10^-3 = 1/2 × 18V/cm × (e/M) × (10/3 × 10^-9)²

or, 2× 10^-3 = 900 × 100/9 × 10^-18 × (e/m)

or, 2 × 10^-3 = 10^-14 × (e/m)

or, 2 × 10¹¹ = (e/m)

hence, e/m = 2 × 10¹¹ C/Kg

Answer 2

Answer:

e/m = 2 × 10¹¹ C/Kg

Explanation:

Let electron moves along x axis with constant velocity v, due to present of electric along y axis, electron deflected from its path.

Let t is time taken to travel x distance with speed v m/s by electron .

so, x = vt

=> t = x/v

= 0.1/(3 × 10^7)

= 10/3 × 10^-9sec

now, deflection of electron in y axis :

y = 1/2 at²

or, 2mm = 1/2 × a × t²

using, F = ma = qE

or, a = qE/m = eE/m

so, 2mm = 1/2 × (eE/m)t²

or, 2 × 10^-3 = 1/2 × 18V/cm × (e/M) × (10/3 × 10^-9)²

or, 2× 10^-3 = 900 × 100/9 × 10^-18 × (e/m)

or, 2 × 10^-3 = 10^-14 × (e/m)

or, 2 × 10¹¹ = (e/m)

hence, e/m = 2 × 10¹¹ C/Kg