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

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To find the electric field at a point 0.130 m outside a solid metal sphere with a radius of 0.4 m and a charge of 0.190 nC, the correct approach involves using Gauss's Law. The equation EA = q/ε₀ is applied, where E is the electric field, A is the surface area, and q is the charge. The radius used in calculations should be the total distance from the center of the sphere to the point of interest, which is 0.4 m + 0.130 m. After correcting arithmetic errors, the calculated electric field value is 6.079 N/C, which aligns with the expected result. Proper use of parentheses and careful arithmetic are crucial for accurate calculations.
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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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