Point Charge and Charged Sphere

[ThirdEyeBlind]

Homework Statement

A point charge q1 = -7 μC is located at the center of a thick conducting shell of inner radius a = 2.6 cm and outer radius b = 4.9 cm, The conducting shell has a net charge of q2 = 1.1 μC.

What is Ex(P), the value of the x-component of the electric field at point P, located a distance 8.9 cm along the x-axis from q1?

Homework Equations

(1.)For an electric field outside of a conducting sphere(where r>R), E=Q/ (4pi Epsilon naught r^2)
(2.)Electric Field of Point Charge, E= kQ/r^2

The Attempt at a Solution

OK, so what I did was try to the sum of the electric fields first from the point charge in the center using equation (2.) and then I added that to the electric field outside the sphere to the point using equation (1.) and my Q as q2.
Doing this I get -1774598 N/C when the answer should be -6703699 N/C. I am not very good at E&M so I would appreciate all help.

 

[tiny-tim]

Hi ThirdEyeBlind!

(try using the X² and X₂ icons just above the Reply box )

Hint: what is the electric field outside a sphere of radius > b ?

 

[ThirdEyeBlind]

Alright so now I am getting the correct answer thanks to your hint but I am now stuck on another part.

What is σb, the surface charge density at the outer edge of the shell?
I was just thinking it would have been (1.1E-6 C) / (.049 m² - .026 m² * pi)
which is the charge of the conducting shell divided by the area of the shell. However the answer is -0.00019554 C/m² so I don't understand how they get that.

 

[tiny-tim]

Hi ThirdEyeBlind!

(just got up :zzz: …)

What is σb, the surface charge density at the outer edge of the shell?
I was just thinking it would have been (1.1E-6 C) / (.049 m² - .026 m² * pi)
which is the charge of the conducting shell divided by the area of the shell.

Sorry, but this is completely wrong.

For the surface charge density at the outer edge, you use only the area of the outer edge (isn't that obvious? ).

Also, it's 4πr² for the area, not πr².

Also, you need to find the charge on the outer edge, not the net charge.