Question

A single point charge is placed at the center of an imaginary cube that has 30 cm long edges. The electric flux out of one of the cube's sides is -3.1 kN·m^2/C. How much charge is at the center?

Answer 1

- 1.65 × 10⁻⁷ C

Step-by-step explanation:

Given:

Sides of the cube = 30 cm long

Electric flux, φ = - 3.1 kN.m²/C = - 3.1 × 10³ N.m²/C

Now,

For the cube,

The charge using the Gauss law is given as:

q = ε₀ × (nφ)

Here,

q is the charge

ε₀ = 8.85 × 10⁻¹² C²/N.m²

n is the number of sides for the cube = 6

Thus,

q = 8.85 × 10⁻¹² × 6 × (- 3.1 × 10³ )

or

q = - 1.65 × 10⁻⁷ C