Question

How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 20.0 cm in diameter to produce an electric field of 1450 N/C just outside the surface of the sphere

Answer 1

1.007 × 10^(10) electron

Step-by-step explanation:

We are given;

Electric Field;E = 1450 N/C

Diameter;d = 20 cm = 0.2 m

So, Radius: r = 0.2/2 = 0.1 m

Formula for Electric field just outside the sphere is given by the formula;

E = kq/r²

Where;

E is the magnitude of the electric field. q is the magnitude of the point charge r is distance from the point charge

k is a constant with a value of 9 x 10^(9) N.m²/C²

Making q the subject, we have;

q = Er²/k

Thus,

q = 1450 × 0.1²/(9 × 10^(9))

q = 1.61 × 10^(-9) C

Now, total charge q is also given by the formula;

q = Ne

Where;

e is charge on electron which is 1.6 × 10^(-19)

N is number of excess electrons

Making N the formula, we have;

N = q/e

N = (1.61 × 10^(-9))/(1.6 × 10^(-19))

N = 1.007 × 10^(10) electron