Gauss' Law with Calculus Video Lessons

Concept

# Problem: A solid conducting sphere with radius R that carries positive charge Q is concentric with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly over the insulating shell.Part A. Find the direction of the electric field in the region 0 &lt; r &lt; R.a. radially inwardb. radially outwardc. the field is zeroPart B. Find the magnitude of the electric field in the region R &lt; r &lt; 2R.Express you answer in terms of the variables R, r, Q, and constants π and e0.Part C. Find the direction of the electric field in the region R &lt; r &lt; 2R/a. radially inwardb. radially outwardc. the field is zero

###### FREE Expert Solution

In this problem, we need to know Gauss's law expressed as:

$\overline{){{\mathbf{\varphi }}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\int }}{\mathbf{E}}{\mathbf{·}}{\mathbf{dA}}{\mathbf{=}}\frac{{\mathbf{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}{{\mathbf{\epsilon }}_{\mathbf{0}}}}$, where E is the electric field, A is the area of the Gaussian surface, Qenc is the enclosed charge, and ε0 is the permittivity of space.

Part A

The charge enclosed in the sphere is zero.

From Gauss's law:

83% (414 ratings)
###### Problem Details

A solid conducting sphere with radius R that carries positive charge Q is concentric with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly over the insulating shell.

Part A. Find the direction of the electric field in the region 0 < r < R.
c. the field is zero

Part B. Find the magnitude of the electric field in the region R < r < 2R.
Express you answer in terms of the variables R, r, Q, and constants π and e0.

Part C. Find the direction of the electric field in the region R < r < 2R/