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Two thin square flat sheets are placed parallel to each other.The distance between the sheets is much smaller than the size ofeach sheet, so we can consider the sheets infinite. The sheets areuniformly charged, with surface charge densities σ1 and σ2,respectively. The magnitudes and the signs of these chargedensities are not known. To determine σ1 and σ2, you measure theelectric force on a test point charge q = 2.00 nC at severallocations. You find the following results:

i) When the test charge is placed in the region between thesheets, the electric force is 7.92 mN (mili Newtons) and isdirected towards sheet 2.

ii) When the test charge is placed in the regions outside, oneither side of the sheets, the electric force is 1.12 mN and isdirected towards the sheets.

Now address the following questions:

a) Calculate the electric field in the region between the sheetsand then in the outside regions. Draw the sheets and sketch someelectric field lines in all three regions.
Show neatly your calculations. (15 points)

b) Determine σ1 and σ2. Express your results for σ1 and σ2 innC/cm2 and do not forget to include the sign. Show neatly yourcalculations. (20 points)
(Hint: start by expressing the electric fields you just calculatedin part a in terms of σ1 and σ2, keeping in mind the principle ofsuperposition. Then solve for the charge densities.)

[Formulas to use: Esheet = 2πk|σ|; F = qE, and the principle ofsuperposition]