Question

A pair of charged conducting plates produces a uniform field of 19800 N/C, directed to the right, between the plates. The separation of the plates is 320 mm. An electron is projected from plate A, directly toward plate B, with an initial speed of v0 = 8.7 x 107m/s.
What is the speed of the electron as it strikes plate B? (include units with answer)

Answer 1

Electric field between two conducting plates, E = 19800 N/C

Separation between two plates, d = 320 mm = 0.32 m

Mass of electron, m = 9.11 x 10^-31 kg

Initial speed of electron, v_o = 8.7 x 10⁷m/s.

Acceleration of electron, a = eE/m = 1.6 x 10^-19 x 19800/9.11 x 10^-31

Acceleration, a = 3.47 x 10¹⁴ m/s²

The acceleration of the electron is negative assuming that it is shot along the electric field.

If V is the velocity of electron as it strikes the plate B,

V² = V₀² – 2ad = (8.7 x 10⁷)² – 2 x 3.47 x 10¹⁴ x 0.32 = 73.47 x 10¹⁴

V = 8.57 x 10⁷ m/s

the velocity of electron as it strikes the plate B, V = 8.57 x 10⁷ m/s