Answer to Question #128550 in Physics for Petricci

Question

A spherical matter of radius 1 m, which carries a charge of +1 μC at its center, is enclosed by a Gaussian surface.
i. What is the electric flux through the Gaussian surface?

ii. Determine the permittivity of the Gaussian surface. [k = 8.99 x 109 Nm2
/C2, π = 22/7]

Answer 1

i.

$\Phi=\int EdA=\frac{q}{\epsilon_0}=4\pi kq=4\cdot\frac{22}{7}\cdot8.99\cdot10^9\cdot1\cdot10^{-6}=113017(V\cdot m)$

ii.

$\Phi=\frac{q}{\epsilon_0}\to \epsilon_0=\frac{q}{\Phi}=\frac{1\cdot10^{-6}}{113017}=8.85\cdot10^{-12}(F/m)$