Another concentric sphere electric field question

In summary, the conversation revolves around a question about finding the electric field of two concentric plastic spherical shells with uniformly distributed charges. After some confusion about the assumptions made in the previous question, the correct solution is determined to be no field inside the smaller shell, the same negative field as the previous question between the shells, and no field outside the larger shell due to the cancellation of the charges.
  • #1
tony873004
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[SOLVED] another concentric sphere electric field question

Interestingly, the very next question does specify uniformly distributed charges. This inconsistency has me worried that we were not to make that assumption in the 1st question from the other thread. Time to visit the office hours!

Homework Statement


Two concentric plastic spherical shells carry uniformly distributed charges, Q on the inner shell and –Q on the outer shell. Find the electric field (a) inside the smaller shell, (b) between the shells, and (c) outside the larger shell.

The Attempt at a Solution


I imagine the answer for (a) is no field, (b) is same as the previous question, only negative:[tex]
\overrightarrow E = \frac{{ - Q}}{{4\pi r^2 \varepsilon _0 }}{\rm{\hat r}}
[/tex]

But I'm not sure about (c). I'm guessing it would be
[tex]
\overrightarrow E = \frac{Q}{{4\pi r_1^2 \varepsilon _0 }}{\rm{\hat r }} - \frac{Q}{{4\pi r_2^2 \varepsilon _0 }}{\rm{\hat r}}
[/tex]
where r1 is the distance to the outer shell and r2 is the distance to the inner shell. Is this right? Is there a better way to express this or to simplify this expression?

Perhaps
[tex]
\overrightarrow E = \frac{1}{{4\pi \varepsilon _0 }}\left( {\frac{Q}{{r_1^2 }}{\rm{\hat r }} - \frac{Q}{{r_2^2 }}} \right){\rm{\hat r}}
[/tex]




Homework Equations


 
Last edited:
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  • #2
Ans to (a) is correct.

Why is there a minus sign is (b)? The charge on the inner shell is +Q...

In (c), you have goofed up badly. In the other thread, what did you mean by r? I'm leaving it to you to clear the mess up.
 
Last edited:
  • #3
Thanks for your reply. I see the point you're making about r. They should be the same because they are the distance from the center of the spheres to a point of interest, rather than the radius of each sphere.

Ok, new attempt. Outside the spheres, they both reduce to a point charge. So they cancel each other. There are no field lines outside the outer sphere.
 
  • #4
You have got it. [And no minus sign in (b).]
 

Related to Another concentric sphere electric field question

1. What is a concentric sphere electric field?

A concentric sphere electric field is a type of electric field that is created by a point charge located at the center of two or more nested spheres. The electric field lines emanating from the point charge are perpendicular to the surface of the spheres and form concentric circles around the charge.

2. How does the electric field strength change as you move away from the point charge?

The electric field strength decreases as you move away from the point charge. This is because the electric field lines spread out as they move away from the point charge, resulting in a weaker electric field at greater distances.

3. How is the electric field strength related to the charge of the point charge?

The electric field strength is directly proportional to the charge of the point charge. This means that as the charge of the point charge increases, the electric field strength also increases proportionally.

4. Can the electric field lines cross each other in a concentric sphere electric field?

No, the electric field lines cannot cross each other in a concentric sphere electric field. This is because if the lines were to cross, it would mean that the electric field has two different values at the same point, which is not physically possible.

5. How can I calculate the electric field strength at a specific point in a concentric sphere electric field?

To calculate the electric field strength at a specific point, you can use the equation E = kq/r^2, where E is the electric field strength, k is the Coulomb's constant, q is the charge of the point charge, and r is the distance from the point charge to the specific point. You can also use this equation to calculate the electric field strength at different points and compare the results.

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