Conducting sphere Find the electric filed for r<a,a<r<b,r>b

In summary, the conversation discusses the formulas for the electric field for different values of r and how the charge enclosed in the surface is used in the calculations. The speaker is confused about the use of variables, but acknowledges that the concept is correct.
  • #1

Homework Statement



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Homework Equations



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The Attempt at a Solution


for part ii)
a<r<b E=0
I am not sure what will be the difference between the formulas for the electric field for a<r and a>b I think the formulas will look the same:
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The only difference that I can think of is that when r<a, we are going to use the charge enclosed in that surface. For r>b we are going to use the total charge. Is that true?
 

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  • #2
I'm confused on your use of variables, but looks like you got the right idea. You're correct, Qenc refers to total charge enclosed within the closed surface you're integrating over.
 
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Likes Jozefina Gramatikova

1. What is a conducting sphere?

A conducting sphere is a spherical object made of a material that allows electric charges to move freely throughout its surface. This means that the charges can redistribute themselves evenly on the surface of the sphere, resulting in a uniform electric field inside the sphere.

2. How is the electric field calculated for a conducting sphere?

The electric field for a conducting sphere can be calculated using the formula E = Q/(4πεr²), where Q is the charge on the sphere, ε is the permittivity of the surrounding medium, and r is the distance from the center of the sphere. This formula applies for all values of r, including inside the sphere (r < a), on the surface of the sphere (a < r < b), and outside the sphere (r > b).

3. What happens to the electric field inside a conducting sphere?

Inside a conducting sphere, the electric field is zero. This is because the charges on the surface of the sphere redistribute themselves to cancel out any external electric field. As a result, the net electric field inside the sphere is zero.

4. How does the electric field change as the distance from the center of the sphere increases?

As the distance from the center of the sphere increases, the electric field decreases. This follows the inverse square law, meaning that the electric field decreases proportionally to the square of the distance. This relationship holds true for all values of r, including inside the sphere, on the surface, and outside the sphere.

5. What is the significance of the radius values in the formula for the electric field of a conducting sphere?

The radius values, a and b, represent the boundaries of the conducting sphere. Inside the sphere (r < a), the electric field is zero. On the surface of the sphere (a < r < b), the electric field is non-zero and depends on the charge and radius of the sphere. Outside the sphere (r > b), the electric field follows the inverse square law with respect to the distance from the center of the sphere.

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