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Chapter 22: Problem 46

Four charges are placed in a three-dimensional space. The charges have magnitudes \(+3 q,-q,+2 q,\) and \(-7 q .\) If a Gaussian surface encloses all the charges, what will be the electric flux through that surface?

Short Answer

Expert verified
Answer: The electric flux through the Gaussian surface is \(\frac{-3q}{\varepsilon_0}\).

Step by step solution

01

Determine the net charge enclosed by the Gaussian surface

To find the net charge enclosed by the Gaussian surface, we will sum all the charges within the surface: \((+3q) + (-q) + (+2q) + (-7q)\).
02

Calculate the net charge

Now we will calculate the total charge: \(+3q - q + 2q - 7q = -3q\).
03

Apply Gauss's Law

With the net charge enclosed by the Gaussian surface, we can find the electric flux using Gauss's Law: \(\Phi_E = \frac{Q_{enclosed}}{\varepsilon_0}\).
04

Calculate the electric flux

The net charge is \(-3q\), so the electric flux through the Gaussian surface is: \(\Phi_E = \frac{-3q}{\varepsilon_0}\). Thus, the electric flux through the Gaussian surface is \(\frac{-3q}{\varepsilon_0}\).

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