Question 23.36: Figure 23-47 shows cross sections through two large, paralle......
Figure 23-47 shows cross sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 1.77 × 10^{-22} C/m². In unit-vector notation, what is \vec{E} at points (a) above the sheets, (b) between them, and (c) below them?
According to Eq. 23-13 the electric field due to either sheet of charge with surface charge density \sigma=1.77 \times 10^{-22}\, C / m ^2 is perpendicular to the plane of the sheet (pointing away from the sheet if the charge is positive) and has magnitude E=\sigma / 2 \varepsilon_0 . Using the superposition principle, we conclude:
E=\frac{\sigma}{2 \varepsilon_0} \quad \text { (sheet of charge). } (23-13)
(a) E=\sigma / \varepsilon_0=\left(1.77 \times 10^{-22} \,C / m ^2\right) /\left(8.85 \times 10^{-12} \,C ^2 / N \cdot m ^2\right)=2.00 \times 10^{-11} \,N / C , pointing in the upward direction, or \vec{E}=\left(2.00 \times 10^{-11}\, N / C \right) \hat{ j } ;
(b) E = 0;
(c) and, E=\sigma / \varepsilon_0 , pointing down, or \vec{E}=-\left(2.00 \times 10^{-11}\, N / C \right) \hat{ j } .