Question

The electric field everywhere on the surface of a thin, spherical shell of radius 0.795 m is of magnitude 889 n/c and points radially toward the center of the sphere. (a) what is the net charge within the sphere's surface

Answer 1

Let's apply Gauss theorem here, taking the surface of the sphere as Gaussian surface. Gauss theorem states that the net electric flux through the surface is equal to the ratio between the net charge Q within the sphere and the electric permittivity:
$E(r) \cdot 4 \pi r^2 = \frac{Q}{\epsilon_0}$
where E(r) is the electric field intensity at distance r from the center of the sphere, and r is the distance from the center of the sphere.

Since we know the radius, r, and the electric field intensity E, we can re-arrange the formula to find the net charge contained in the sphere:
$Q= E 4 \pi \epsilon_0 r^2 = (889 N/C)(4 \pi )(8.85 \cdot 10^{-12} F/m)(0.795 m)^2=$
$=6.2 \cdot 10^{-8} C$