A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries an excess charge of .A point charge of is present at the center.The surface charge density on the inner spherical surface is closest to A) zero. B) +4.0 × 10^-8 C/m². C) +6.0 × 10^-8 C/ m². D) -4.0 × 10^-8 C/ m². E) -6.0 × 10^-8 C/ m².

Question

Quizplus · Accepted Answer

Since the charge is located at the center of the shell, it will induce charges on both inner and outer surfaces of the shell. Since the shell is conducting, the charges will distribute themselves in a way such that there is no electric field inside the shell. This means that the charge on the inner surface of the shell must be equal in magnitude and opposite in sign to the point charge at the center.

Therefore, the surface charge density on the inner surface of the shell can be found using the formula: sigma = Q/A, where Q is the charge on the surface and A is the surface area.

The surface area of the inner surface can be found using the formula for the surface area of a sphere: A = 4πr^2.

Therefore, sigma = (-11.8 nC) / (4π(0.8 m)^2) = -4.07 × 10^-8 C/m^2

The closest answer choice is D, -4.0 × 10^-8 C/m^2.

A Hollow Conducting Spherical Shell Has Radii of 0