What is the electric field 4cm from a uniformly charged plate?

AI Thread Summary
The electric field 4cm from a uniformly charged plate is 30 N/C, which remains constant regardless of distance from the plate. This is because the electric field produced by an infinite plane of charge is independent of distance, unlike that of a point charge. The initial confusion arose from incorrectly applying the point charge formula E=kq/r^2, which does not apply to a charged plate. The correct formula for a sheet of charge shows that the electric field is determined by charge density and is constant. Understanding this concept clarified the solution for the problem.
roflcopter
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Homework Statement


Charge is distributed uniformly on the surface of a large flat plate. The electric field 2cm from the plate is 30 N/C. The electric field 4cm from the plate is:

A. 120 N/C
B. 80 N/C
C. 30 N/C
D. 15 N/C
E. 7.5 N/C

Homework Equations



E=kq/r^2 (possibly)

The Attempt at a Solution



Well, the answer I got was E, 7.5 N/C. I got that by using the above equation, plugging in 30 for E and 2 for r and solving for q. Then, I used that same value of q and the new r to solve for E and got 7.5 N/C. Supposedly the correct answer is C, 30 N/C. I don't understand how they got that though. Why is the E field still the same? Shouldn't it be decreasing with the greater distance?

Anyways, I think I might be wrong because I remembered afterwards that E=kq/r^2 is the E field due to a point charge and not a plate...maybe that's why I got the wrong answer?
 
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roflcopter said:
... I remembered afterwards that E=kq/r^2 is the E field due to a point charge and not a plate...maybe that's why I got the wrong answer?

I think you are on to something.

What is the field of a sheet of charge?
 
LowlyPion said:
I think you are on to something.

What is the field of a sheet of charge?

Oh. I believe it's in here: http://230nsc1.phy-astr.gsu.edu/hbase/electric/elesht.html

So the eq looks like E=charge density/2*epsilon. So this is independent of distance. I see.
 
Yep. Thanks for the help!
 
Actually you solved it yourself.

The best outcome of all.
 
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