\"A test charge of 1.30 ?C is placed 7.30 cm away from a large flat uniformly ch

Question

"A test charge of 1.30 ?C is placed 7.30 cm away from a large flat uniformly charged nonconducting surface. The force on the charge is 260 N. The charge is now moved to 1.70 cm away from the surface. What is the force on the test charge now?"

MY PROBLEM: Now, I know the answer is 260N because E and q do not change. However, I am trying to figure this out from the hints that were given so that this problem makes sense to me.

One of the hints was to find charge density [sigma], which is defined as a ratio of a total charge of a charged sheet Q{sheet} over its area A{sheet}, i.e.sigma=Q{sheet}/A{sheet}. However, how do you know what Q and A is? Is Q just 1.30 uC? What would the area of the sheet be?

If I can figure this out, I may be able to understand the problem. Thank you!

Explanation / Answer

If the sheet is very large (compared to the distance of the point charge from it) and uniformly charged, then the electric field actually will vary negligibly with the distance from the sheet, that is, the electric field produced will be very nearly uniform. This is the same reason that, very close to the Earth's surface, the gravitational field is almost perfectly uniform. Knowing that the electric field is uniform should be enough for you to answer the problem.

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