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?
the positive charge has a spherically symmetric charge distribution or
the negative charge has a spherically symmetric charge distribution or
the negative charge has an asymmetric charge distribution or
the positive charge has an asymmetric charge distribution

To find the net charge within the spherical shell's surface, we can use Gauss's Law.

(a) To apply Gauss's Law, we need to know the total electric flux passing through the surface of the sphere. The electric flux is given by the product of the electric field and the surface area. Since the electric field points radially inward, the electric flux will be negative.

The formula for electric flux (Φ) is given by:

Φ = E * A

where E is the electric field and A is the surface area.

The surface area of a sphere is given by:

A = 4πr^2

where r is the radius of the sphere.

Given that the electric field (E) is 860 N/C and the radius (r) is 0.710 m, we can substitute these values into the formulas:

A = 4π(0.710^2) = 7.982 m^2

Φ = (860 N/C) * (-7.982 m^2) = -6857.32 N * m^2 / C

The negative sign indicates that the electric flux is pointing inward.

Now, according to Gauss's Law, the electric flux passing through a closed surface is equal to the product of the net charge enclosed within the surface and the electric constant (ε0). Therefore, we can set up the following equation:

Φ = q / ε0

where q represents the net charge within the spherical shell's surface and ε0 is the electric constant.

Rearranging the equation, we get:

q = Φ * ε0

The value of ε0 is approximately 8.85 x 10^-12 C^2 / (N * m^2).

Substituting the values, we can calculate the net charge (q):

q = (-6857.32 N * m^2 / C) * (8.85 x 10^-12 C^2 / (N * m^2))
≈ -6.06 x 10^-8 C

Therefore, the net charge within the sphere's surface is approximately -6.06 x 10^-8 C (negative charge).

(b) Based on the given information, we can conclude that the charge inside the spherical shell has a spherically symmetric charge distribution with negative charge. This is because the electric field points radially inward at every point on the surface, indicating that the source of the electric field is negative charge distributed symmetrically within the shell.