Answer to Question #140087 in Electricity and Magnetism for Innocent

Question #140087
A spherical Gaussian surface of radius a = 400 cm surrounding a -50 µC charge. Find the
flux through
1
Expert's answer
2020-10-25T18:31:29-0400

By definition, the flux of electric field is

"\\Phi = E \\cdot S"

Here E is a vector of electric field and S is a vector which module is equal to the area of the surface and direction is normal to the surface.

For the point-like charge and the sphere which surrounds it, the scalar product will "E \\cdot S = |E| |S|" since the vectors have the same direction.

"\\displaystyle E = \\frac{1}{4 \\pi \\epsilon_0} \\frac{q}{r^2}"

"S = 4 \\pi r^2"

"\\displaystyle \\Phi = ES = \\frac{q}{\\epsilon_0} = - \\frac{50 \\cdot 10^{-6}}{8.85 \\cdot 10^{-12}}= 5.65 \\cdot 10^6 \\; \\; [\\frac{N \\cdot m^2}{C}]"


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