An electron is initially at ground level, and the electric potential at that poi

Question

An electron is initially at ground level, and the electric potential at that point is assumed to be exactly 0. The electron is immersed in a uniform electric field that points down with a magnitude of 2.7x10^ -11 N/C as well as Earth's graviational field (9.8 N/kg pointing down). Only gravity and the electric force are relevant.

a) If the electron is given an initial upward speed of 30 m/s, what is the maximum height above the ground that it will reach?

b) What is the change in electric potential energy during this motion (final - initial)?

c) How much work is done by the electric force during this motion?

d) What is the voltage at the electron's maximum height?

Explanation / Answer

a)

q = magnitude of charge on electron = 1.6 x 10-19

E = electric field = 2.7 x 10-11

m = mass of electron = 9.1 x 10-31

force equation is given as

qE - mg = ma

(1.6 x 10-19) (2.7 x 10-11) - (9.1 x 10-31) (9.8) = (9.1 x 10-31) a

a = - 5.1 m/s2

Vi = initial velocity = 30 m/s

Vf = final velocity = 0 m/s

h = maximum height gained

using the equation

Vf2 = Vi2 + 2 a h

02 = 302 + 2 (- 5.1) h

h = 88.2 m

b)

change in electric potential energy is given as

U = q E h = (- 1.6 x 10-19) (2.7 x 10-11) (88.2) = - 3.8 x 10-28 J

c)

work done by electric force = U = - 3.8 x 10-28 J

d)

V = E h = (2.7 x 10-11) (88.2) = 2.4 x 10-9 Volts

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