Careful measurement of the electric field at the surface of a black box indicates that thenet outward flux through the surface of the box is3 29 10 /Nm C . What is theapproximate net charge inside the box?
Question
Careful measurement of the electric field at the surface of a black box indicates that thenet outward flux through the surface of the box is3 29 10 /Nm C . What is theapproximate net charge inside the box?
Solution
To find the net charge inside the box, we can use Gauss's Law. Gauss's Law states that the net outward flux through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space (ε₀).
The formula for Gauss's Law is:
Φ = Q / ε₀
Where: Φ is the electric flux, Q is the net charge, and ε₀ is the permittivity of free space, which is approximately 8.85 x 10^-12 C^2/Nm^2.
Given that the net outward flux (Φ) is 3.29 x 10^10 Nm^2/C, we can rearrange the formula to solve for Q:
Q = Φ * ε₀
Substituting the given values:
Q = (3.29 x 10^10 Nm^2/C) * (8.85 x 10^-12 C^2/Nm^2)
Solving for Q gives us the approximate net charge inside the box.
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