Answer to Question #170716 in Molecular Physics | Thermodynamics for kebron tefera

Question

Consider four uniformly charged plates oriented normal to the x-axis as shown. The drawing scale exaggerates the size of the

lengths along x compared to sizes along y

and z. Let L=1.0m, d=1.0mm, Q1=3.0C,

Q2=-3.0C, Q3=8.0C, and Q4=-6.0C. The positions of the plates are at x1, x2, x3 and x4.

1. a) Find the 2D charge density of each plate
2. b) Findthenetelectricfieldinregion
3. x2 <x<x3. 

Answer 1

Plate area, $A=l \times d = 1*10^{-3}= 10^{-3} m^2$

Charge density of first plate, $\sigma_1=\frac{q_1}{A}=\frac{3}{10^{-3}}=3\times 10^{-3} Cm^{-2}$

Charge density on second plate, $\sigma_2=\frac{q_2}{A}=\frac{-3}{10^{-3}}=-3\times 10^{-3} Cm^{-2}$

Charge density on third plate, $\sigma_3=\frac{q_3}{A}=\frac{8}{10^{-3}}=8\times 10^{-3} Cm^{-2}$

Charge density on fourth plate, $\sigma_4=\frac{q_4}{A}=\frac{-6}{10^{-3}}=-6\times 10^{-3} Cm{-2}$

Let separation between the plates is 1m.

Electric field is given by, $E =\frac{\sigma_1- \sigma_2- \sigma_3+ \sigma_1 }{\epsilon_0}=\frac{(3-3-8+6)*10^{3}}{8.85*10^{-12}} = 0.226*10^{9} N/C$