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.

 

[rwisz]

I would suggest first checking your calculations and making sure you are using the correct units for charge and distance. It is also important to note that the net charge of the conducting shell will not affect the electric field at point P, as it is located outside of the shell. Therefore, you only need to consider the electric field from the point charge q1.

Next, I would recommend using the superposition principle, which states that the total electric field at a point is the vector sum of the individual electric fields from each source charge. In this case, you can use equation (2.) to calculate the electric field from q1 at point P, and then add it to the electric field from q2 at point P (using equation (1.) with q2 as the source charge).

I would also suggest drawing a diagram to visualize the situation and make sure you are using the correct distances and directions for your calculations.

If you are still having trouble, you can also consult a textbook or seek help from a professor or tutor. It is important to understand the fundamental principles and equations in electromagnetism in order to accurately solve these types of problems.