Magnitude of the Electric Field at the Following Distances

[Darkgora]

Homework Statement

The figure below shows a spherical shell with uniform volume charge density ρ = 1.87 nC/m3, inner radius a = 15.0 cm, and outer radius b = 2.60a.

[Reference Picture]

What is the magnitude of the electric field at the following radial distances?

Homework Equations

E=k(q/r^2)
E=k(q/R^3)*r^2

The Attempt at a Solution

I only understand how to compute an electric field for a solid sphere. I am unsure how to alter the given equation to compensate for the cavity within the charged spherical shell.

 

[andrewkirk]

The shell theorem is used to answer questions like this. It enables one to ignore spherically-distributed charge at distance greater than r from the centre of the sphere, and the rest of the charge can be assumed to be at the centre of the sphere..

 

[kuruman]

Here is an alternative approach. Since you understand the electric field due to a solid sphere, for this problem consider the superposition of the electric fields from two concentric solid spheres, one of radius b and charge density +ρ and one of radius a and charge density -ρ.

 

[Darkgora]

Here is an alternative approach. Since you understand the electric field due to a solid sphere, for this problem consider the superposition of the electric fields from two concentric solid spheres, one of radius b and charge density +ρ and one of radius a and charge density -ρ.

I am unsure how to compute the electric field given charge density, thus I have solved for the total charge enclosed:

Volume of hollow sphere * Charge Density
= 4(pi)/3(.351^3-.13^3) * (1.89e-9)

When I plug this total enclosed charge value into kqr/R^3 and subtract the inner from outer sphere I am not getting the right answer.

 

[kuruman]

When I plug this total enclosed charge value into kqr/R^3 and subtract the inner from outer sphere I am not getting the right answer.

You missed the point of my suggestion. Follow these steps for the field in parts d -f.
1. Find the field due to a solid sphere of charge density -ρ and radius a at that radius.
2. Find the field due to a solid sphere of charge density +ρ and radius b at that radius.
3. Add the fields (one is positive the other negative).

Reference: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html