Electric field and gaussian surface

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Homework Help Overview

The discussion revolves around the electric field behavior in a system consisting of a small charged copper spherical BB at the center of a larger hollow copper spherical shell. The problem involves determining the electric field in various regions, applying Gauss's Law, and understanding the implications of charge distribution within conductors.

Discussion Character

  • Conceptual clarification, Assumption checking, Exploratory

Approaches and Questions Raised

  • Participants explore the electric field within the BB and the hollow shell, questioning whether the field is zero in these regions due to the properties of conductors. They discuss the implications of Gauss's Law and the relationship between electric flux and charge distribution.

Discussion Status

There is a productive exploration of the electric field within the conductor, with multiple participants suggesting that the electric field is zero in the specified regions. Questions about the total flux through a Gaussian surface and the charge distribution on the inner and outer surfaces of the shell are also raised, indicating a collaborative effort to clarify these concepts.

Contextual Notes

Participants are working under the assumption that the total charge of the copper shell is zero, which influences their reasoning about charge distribution and electric fields within the conductors.

PinkFlamingo
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A small copper spherical BB of radius a is located at the center of a larer hollow copper spherical shell of inner radius b and outer radius R. A charge of +q is on the small BB. The hollow copper shell has zero charge on it.

a) What is the electric field within the BB (for radii r<a)?

b) What is the electric field inside the copper shell (for radii that stisfy b<r<R)

c) Draw a closed Gaussian surface within the copper of the shell. What is the total flux of the electric vector through this Gaussian surgace? This result implies that charge must lie on the inside surface of the spherical shell. What charge must reside on the inside surgface of the copper shell? Since the copper shell has a total charge of zero, what charge must reside on the outer surface of the copper shell?

Please help me!

So far all I've been able to figure out is that the answer to b is 0 I think?
 
Last edited:
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These questions require you to know two things:
(1) The electrostatic field within a conductor is zero
(2) Gauss's Law, which relates the total electric flux through a closed surface to the charge within that surface

Can you state Gauss's Law? How do you apply it?
 
Would the answer to a AND b be 0 because they're both within the conductor?
 
PinkFlamingo said:
Would the answer to a AND b be 0 because they're both within the conductor?
Yes. The field within both conductors is zero.
 
Would the answer to c be 0 as well, since the total charge is 0, the flux must be 0 too right?
 
PinkFlamingo said:
Would the answer to c be 0 as well, since the total charge is 0, the flux must be 0 too right?
See my comments:
c) Draw a closed Gaussian surface within the copper of the shell. What is the total flux of the electric vector through this Gaussian surgace?
Since it's within a conductor, the field and flux must be zero.
This result implies that charge must lie on the inside surface of the spherical shell. What charge must reside on the inside surgface of the copper shell?
So what charge must lie on the inside surface? Remember: Total charge within the Gaussian surface must be zero.
Since the copper shell has a total charge of zero, what charge must reside on the outer surface of the copper shell?
The charge on the inner surface plus the charge on the outer surface must add to zero. Figure it out.
 

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