Gauss' Law with Calculus Video Lessons

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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 < r < R.a. radially inwardb. radially outwardc. the field is zeroPart 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/a. radially inwardb. radially outwardc. the field is zero

FREE Expert Solution

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

ϕE=E·dA=Qencε0, 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:

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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.
a. radially inward
b. radially outward
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/
a. radially inward
b. radially outward
c. the field is zero

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