Solving Gauss's Law Problem: Find Electric Field at Point

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Homework Help Overview

The problem involves applying Gauss's Law to determine the electric field at a point outside a charged solid metal sphere. The original poster presents a specific scenario with a sphere of radius 0.4 m and a net charge of 0.190 nC, seeking to find the electric field at a distance of 0.130 m from the sphere's surface.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply Gauss's Law and expresses uncertainty about their calculations and the correct interpretation of the radius in the context of the problem. Some participants question the arithmetic used in the calculations and the values chosen for the radius.

Discussion Status

The discussion is ongoing, with participants providing feedback on the calculations. There is a recognition of potential arithmetic errors, and the original poster has acknowledged making a mistake in their calculations, leading to a revised answer.

Contextual Notes

Participants are exploring the correct interpretation of the radius in relation to the electric field calculation, considering whether to use the radius of the sphere, the distance from the center to the point of interest, or a combination of both. There is an emphasis on ensuring proper use of parentheses in calculations.

eku_girl83
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Here's the homework problem I'm having trouble with:
A solid metal sphere of radius .4 m carries a net charge of .190nC. Find the magnitude of the electric field at a point .130 m outside the surface of the sphere.

I used the equation EA=q/Epsilon_0
E(4*pi)(r^2)=q/Epsilon_0
E(4*pi)(.130+.4)^2=(.190E-9)/(8.854E-12)
E on the right hand side of equation is used to denote scientific notation.
Solving for the electric field I get 75.748 N/C.
Am I doing this correctly?
Any feedback would be appreciated!
 
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Your work looks correct, but your conclusion does not. I think you must have simply made an arithmetic mistake.

- Warren
 
Why does my conclusion seem incorrect?
 
Because I don't see how you solved the equation for E and got the value you got. It looks to me like you simply made a mistake in your arithmetic. Make sure you use parentheses appropriately.

- Warren
 
Am I using the correct value for the radius? Should r=.4+.13, r=.4, or r=.13?
I did make an error in calculations, though. I now get 6.079 N/C.
 
I get the same answer.

- Warren
 

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