Question

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

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

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

Now address the following questions:

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

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

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

Answer 1