The electric field everywhere on the surface of a thin, spherical shell of radius 0.710 m is measured to be 860 N/C and points radially toward the center of the sphere.

(a) What is the net charge within the sphere's surface?
nC
(b) What can you conclude about the nature and distribution of the charge inside the spherical shell?

To find the net charge within the spherical shell, we can use Gauss's law, which states that the total electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the electric constant (ε₀).

(a) The electric field on the surface of the spherical shell is given as 860 N/C. The electric flux through a closed surface can be calculated using the formula:

Electric Flux = Electric Field * Surface Area

The surface area of a sphere is given by the equation: Surface Area = 4πr², where r is the radius of the sphere.

Since the electric field is constant on the entire surface and points radially toward the center, the electric flux will also be constant and equal to 860 N/C * 4π(0.710 m)².

The net charge enclosed within the spherical shell can be calculated using the formula:

Net Charge = Electric Flux * Electric Constant (ε₀)

The value of ε₀ is approximately 8.854 x 10⁻¹² C²/(N·m²).

Now we can use these formulas to calculate the net charge:

Net Charge = (860 N/C * 4π(0.710 m)²) * (8.854 x 10⁻¹² C²/(N·m²))

Calculating this expression will give you the net charge within the spherical shell in coulombs (C).

(b) Since the electric field points radially toward the center of the sphere, it suggests that the charge distribution inside the shell is uniform. This means that the charge is evenly distributed throughout the shell's volume rather than concentrated at a specific point or region.