Electric field at the point within the sheet

[cupcake]

Homework Statement

A huge (effectively infinite) horizontal nonconducting (epsilon = epsilon_0) sheet 10 cm thick has charge over both faces. The upper face carries a uniform +95 nC/m^2 while the lower face carries a uniform -25.0 nC/m^2. The magnitude of the electric field at a point within the sheet 2.00 cm below the upper face is closest to :

Homework Equations

E= k q/r^2

The Attempt at a Solution

Etotal = E1 + E2

E1 = k q1 / r^2 = 9 * 10^9 * 95 *10^-9 / (0.02)^2 = 2137500

E2 = k q2 / r^2 = 9 * 10^9 * 25 *10^-9 / (0.08)^2 = 35156.25

Etotal = E1+E2 = 2172656.25 N/C

is this correct or not?
Thanks

 

[dx]

Your formula for E is for point charges. For an infinite sheet of charge with surface charge density σ, E is σ/2ε. You can prove this using Gauss' law.

 

[nlightner]

for your question. Your approach is correct. The electric field at a point within the sheet can be calculated by taking the sum of the electric fields due to the charges on both faces of the sheet. However, there is a small error in your calculation for E2. The distance between the point and the lower face of the sheet is 0.08 m, not 0.02 m. So the correct value for E2 would be:

E2 = k q2 / r^2 = 9 * 10^9 * 25 *10^-9 / (0.08)^2 = 625000 N/C

Therefore, the correct value for Etotal would be:

Etotal = E1 + E2 = 2137500 + 625000 = 2762500 N/C

This is the closest value to the magnitude of the electric field at the point within the sheet. Keep up the good work!