What is the electric flux through a sphere that has a radius of 1.00 m and carri

Question

What is the electric flux through a sphere that has a radius of 1.00 m and carries a charge of + 5.00 mu C at its center? The magnitude of the electric field 1.00 m from this charge is found using Equation 23.9: E = k_e 1q/r^2 = (8.99 times 10^9 N middot m^2/C^2) 5.00 times 10^-6 C/(1.00 m)^2 = N/C The field points radially outward and is therefore everywhere perpendicular to the surface of the sphere. The flux through the sphere (whose surface area A = 4 pi r^2) is thus Phi = EA = E(4 pi r^2) N middot m^2/C

Explanation / Answer

from Gauss law,

total flux through the sphere = Qin / e0

Qin = 5 uC = 5 x 10^-6 C

flux = (5 x 10^-6) / (8.854 x 10^-12)

flux = 5.65 x 10^5 N m^2 / C

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E = k q / r^2 = (9 x 10^9)(5 x 10^-6) / 1^2

E = 45000 N/C .....Ans

flux = E (4 pi R^2)

= (45000) (4 pi 1^2)

= 5.65 x 10^5 N m^2 / c

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