Question

An electron passing through Point Ain the electric fieldhad thespeed of 107 m/s and atPoint Bthe speed of2×107m/s.

(a) Determine the electric potential difference between points Aand B.
(b) What would be the electron speed atPoint B, if atPoint Athe speed were zero?

Answer 1

a) Electric potential = 853 V

b) Electron speed at point B, if at Point A, the speed were zero = 1.732 × 10⁷ m/s

Step-by-step explanation:

For an electron moving in an electric field with potential V,

Work done = qV where q is the charge on the electron

And the Work done is equal to the change in kinetic energy of the electron

qV = m(v₂² - v₁²)/2

V = m(v₂² - v₁²)/2q

q = 1.602 × 10⁻¹⁹C

m = 9.11 × 10⁻³¹ kg

v₁= 10⁷ m/s

v₂ = 2 × 10⁷ m/s

Putting these values in for the variables and solving

V = 853 V

b) If the electron started from rest,

qV = mv²/2

v = √(2qV/m) =√((2 × (1.602 × 10⁻¹⁹) × 853)/(9.11 × 10⁻³¹)) = 1.732 × 10⁷ m/s