How Does Gauss' Law Apply to the Electric Field Around a Charged Metal Ball?

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Homework Help Overview

The discussion centers around applying Gauss' Law to determine the electric field generated by a charged metal ball. The problem involves calculating the electric field as a function of the distance from the center of the ball, given specific parameters such as the radius and charge of the ball.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Gauss' Law, particularly how to express the electric field inside and outside the charged metal ball. There is a focus on understanding why the electric field is zero inside the conductor and how it behaves outside as the distance increases.

Discussion Status

The discussion is ongoing, with participants confirming the understanding that the electric field inside the ball is zero. There is also an exploration of the expected behavior of the electric field outside the ball, with some participants questioning the consistency of the derived equations.

Contextual Notes

Participants are working within the constraints of the problem statement and are considering the implications of Gauss' Law in the context of electrostatics. There is a repeated emphasis on the relationship between the radius and the distance from the center of the ball.

kasse
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Homework Statement



A metal ball with radius R = 0,6 m is charged with Q = 0.15 nC. Find the electrical field as function of the distance r from the center of the ball.


The Attempt at a Solution





Gauss law:

Q = e0*E(r)*A = e0*E(r)*4*pi*R^2

which gives

E(r) = Q / e0*4*pi*R^2

I know that inside the ball, the field will be 0. But obviously this is not a function of r...Am I on the right track?
 
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You're fine.

E(r) = 0 for r<R is perfectly acceptable as a function of r.
 
And outside the ball? I would expext the field to decrease with increasing r, not be constant...
 
kasse said:
And outside the ball? I would expext the field to decrease with increasing r, not be constant...
Right. You have that already done in your first post. (Just change R to r in your equation for E.)
 
rajxen

I guess you are correct. The field inside a conductor is zero.

kasse said:

Homework Statement



A metal ball with radius R = 0,6 m is charged with Q = 0.15 nC. Find the electrical field as function of the distance r from the center of the ball.


The Attempt at a Solution





Gauss law:

Q = e0*E(r)*A = e0*E(r)*4*pi*R^2

which gives

E(r) = Q / e0*4*pi*R^2

I know that inside the ball, the field will be 0. But obviously this is not a function of r...Am I on the right track?
 

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