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

Answer:

q₁  = -2.92 nC

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.

$\phi = \frac{q_{enc.}}{\epsilon_o}$

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