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A 8.2 μC charge and a −5.3μC charge are inside an uncharged sphere. What is the electric flux through the sphere?

User Minal Shah
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Final answer:

The electric flux through an uncharged sphere with charges inside it can be calculated using Gauss's law. For charges of 8.2 μC and -5.3 μC inside the sphere, the electric flux is 3.28 x 105 N·m2/C.

Step-by-step explanation:

The student's question is about calculating the electric flux through an uncharged sphere that contains two charges inside it. According to Gauss's law, the electric flux through a closed surface is equal to the net charge enclosed by the surface divided by the vacuum permittivity constant (ε0). Given that the charges inside the sphere are 8.2 μC and -5.3 μC, we calculate the net charge as the sum of these two charges.

The net charge (Q) inside the sphere is the sum of the individual charges: Q = (8.2 μC) + (-5.3 μC) = 2.9 μC, or Q = 2.9 x 10-6 C when converted to coulombs.

Now, applying Gauss's law, the electric flux (ΦE) through the sphere is given by ΦE = Q/ε0, where ε0 is the vacuum permittivity constant (approximately 8.854 x 10-12 C2/N·m2). Substituting the net charge and the vacuum permittivity constant, we find the electric flux.

ΦE = (2.9 x 10-6 C) / (8.854 x 10-12 C2/N·m2) = 3.28 x 105 N·m2/C

Thus, the electric flux through the uncharged sphere is 3.28 x 105 N·m2/C.

User Akarca
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