Question

A Gaussian surface is a closed surface in three-dimensional

space through which the electric flux is calculated. Given a

spherical Gaussian surface that has a radius of 0.5 meters and

encloses 30 electrons.

(a) Find the value of the electric flux through this surface.

(b) From the calculated value of the electric flux, determine the

value of the electric field at a distance equal to 0.6 meters from

the center of the surface.

Answer 1

a)

$$\Phi=\frac{q}{\epsilon_0}\\\Phi=\frac{30(1.6\cdot10^{-19})}{8.85\cdot10^{-12}}=5.4\cdot10^{-7}\ Vm$$

b)

$$E=\frac{\Phi}{4\pi r^2}\\E=\frac{5.4\cdot10^{-7}}{4\pi (0.6)^2}=1.7\cdot10^{-7}\frac{V}{m}$$