Question

A point charge q1 is at the center of a sphere of radius 20 cm. Another point charge q2 = 10 nC is located at a distance r = 10 cm from the center of the sphere. If the net flux through the surface of the sphere is 800 N.m2/C, find q1.

Answer 1

q₁ = -2.92 nC

Step-by-step explanation:

Given;

first point charge, q₁ = ?

second point charge, q₂ = 10 nC

net flux through the surface of the sphere, Φ = 800 N.m²/C

According to Gauss’s law, the flux through any closed surface (Gaussian surface), is equal to the net charge enclosed divided by the permittivity of free space.

`\phi = (q_(enc.))/(\epsilon_o)`

where;

Φ is net flux

`q_(enc.)` net charge enclosed

ε₀ is permittivity of free space.

`q_(enc.)` = Φε₀

= 800 x 8.85 x 10⁻¹²

= 7.08 x 10⁻⁹ C

`q_(enc.)` = 7.08 nC

q₁ + q₂ =
`q_(enc.)`

q₁ =
`q_(enc.)` - q₂

q₁ = 7.08nC - 10 nC

q₁ = -2.92 nC