Electric Fields in Solid Sphere and Thick Shell

[SmokeDragoon]

Homework Statement

What is the electric field at r1, r2, r3 for a solid sphere within a thick spherical shell where r1=1.5cm, r2=5.0cm, r3=8.0cm? The solid sphere has a total charge of 3C and the thick shell has a charge of -9C. a=2.0cm, b=4.0cm, c=6.0cm.
(a=radius of solid sphere, b=inner radius of shell, c=outter radius of shell)

not sure how to calculate/what happens to the electric field when r1 is inside a and b > r3 > c.
they are insulating sphere and shell.

Homework Equations

$$\int_ \vec E. d\vec A = q_\text{enclosed}/\epsilon_0$$
Eo = 8.85 * 10^ -12

The Attempt at a Solution

I solved r3 by using a gaussian surface and using the total charge as a whole.
So then,
EA = q enclosed/Eo
E (4pi(.06)^2) = -6/8.85*10^-12
got E = -1.5*10^13

 

[lippyka]

For r2, I used the same approach but used the total charge of -3C and got E = 5*10^12For r1, I am having trouble. Does the charge of -6C still apply? Or is it just the charge of 3C?If it is just 3C, I got E = 1.5*10^13

 

[m2003]

For r2, I used the same method but just used the charge of the shell.
E (4pi(.05)^2) = -9/8.85*10^-12
got E = -5.1*10^13

For r1, I used the same method but just used the charge of the solid sphere.
E (4pi(.015)^2) = 3/8.85*10^-12
got E = 5.1*10^13

The electric field at r1, r2, and r3 will be affected by the presence of the solid sphere and thick shell. At r1, the electric field will be directed towards the center of the solid sphere due to the positive charge of 3C. At r2, the electric field will be directed towards the center of the thick shell due to the negative charge of -9C. At r3, the electric field will be directed towards the center of the thick shell due to the negative charge of -9C, but it will be weaker compared to r2 due to the larger distance from the center of the shell.

When r1 is inside a and b > r3 > c, the electric field will be affected by the charge distribution of both the solid sphere and the thick shell. The electric field at r1 will be directed towards the center of the solid sphere, but it will also be influenced by the negative charge of the thick shell. This will result in a weaker electric field compared to r1 outside of the shell. At r3, the electric field will be affected by the negative charge of the thick shell, resulting in a weaker electric field compared to r3 outside of the shell. At r2, the electric field will be directed towards the center of the thick shell due to the negative charge, but it will also be influenced by the positive charge of the solid sphere. This will result in a weaker electric field compared to r2 outside of the shell.

To calculate the electric field at r1, r2, and r3, you can use the equation:

E = k*q/r^2

Where k is the Coulomb's constant (9*10^9 N*m^2/C^2), q is the charge of the object, and r is the distance from the center of the object. You will need to consider the charges of both the solid sphere and the thick shell when calculating the electric field at r