Question

How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 30.0 cmcm in diameter to produce an electric field of 1440 N/CN/C just outside the surface of the sphere

Answer 1

1.78×10×10^10 electron

Step-by-step explanation:

Electric field outside the sphere can be calculated using below expression

E= kq/ r^2..........eqn(1)

Where k= 9 × 10^9 NM^2/C^2

q= charge

E= 1440 N/C

Diameter= 30.0 cm= 0.3 m

r= radius= 0.3/2= 0.15m

If we make q subject of formula from eqn(1) we have

q= Er^2/k............eqn(2)

q= 1440 × (0.15)^2 /(9 × 10^9 )

= 2.85×10^-9C

Total charge is an integer of electron charge , then we can calculate the number of the electron using the expression below

q= Ne

Where

N = number of electron

Making N subject of the formula we have

N= q/e

Where e= electron value= 1.6× 10^-19

N=2.85×10^-9 /1.6× 10^-19

= 1.78×10×10^10 electron