Question

A single point charge +Q is at the center of a thin spherical sheet that carries a net charge of – 3Q and has a radius of a. Your goal is to calculate the electric field at a distance r away from the center of the spherical sheet.
(A) Draw the situation below. Represent a in your diagram. You should NOT have r in your diagram.










(B) Use Gauss’s law to calculate the electric field when r < a (i.e., inside the spherical sheet). a. What surface should you use in order to do this? Draw this surface on your diagram above. b. Use Gauss’s law to calculate the electric field inside the spherical shell.









(C) Use Gauss’s law to calculate the electric field when r > a (i.e., outside the spherical shell) a. What surface should you use in order to do this. Draw this surface on the diagram above. b. Use Gauss’s law to calculate the electric field outside the spherical shell.








(D) On the coordinate axes below, plot the electric field magnitude as a function of r. Hint: The electric field is a piece-wise defined function with different expressions in different regions

Answer 1

A)

B)

We will choose a spherical surface of radius "r" such that r < a

b.

Q_enc = Charge enclosed by the gaussian spherical surface = Q

A = Area of the gaussian surface = 4r²

Using Gauss's law

E A = Q_enc /

E (4r²) = Q/

E = Q/(4r²)

C)

a)

We will choose a spherical surface of radius "r" such that r > a

b)

Q_enc = Charge enclosed by the gaussian spherical surface = |Q - 3Q| = 2 Q

A = Area of the gaussian surface = 4r²

Using Gauss's law

E A = Q_enc /

E (4r²) = 2Q/

E = 2Q/(4r²)