Three very large square planes of charge are arranged as shown (on edge) in the

Question

Three very large square planes of charge are arranged as shown (on edge) in the figure. (Figure 1) From left to right, the planes have charge densities per unit area of -0.45 C/m2 , 0.26 C/m2 , and -0.36 C/m2 .

A.Find the total electric field (direction and magnitude) at the point A. Assume the plates are much larger than the distance AD.

B.Find the total electric field (direction and magnitude) at the point B

C.Find the total electric field (direction and magnitude) at the point C

D. Find the total electric field (direction and magnitude) at the point D

Explanation / Answer

electric filed due to this planes is E = q/(2*eo) =

at A

due to left plane

E1 = (0.45*10^-6)/(2*8.85*10^-12) = 25423.72 N/C along +X-axis

due to middle plane

E2 = (0.26*10^-6)/(2*8.85*10^-12) = 14689.3 N/C along -X-axis

due to right plane

E3 = (0.36*10^-6)/(2*8.85*10^-12) = 20339 N/C along +X-axis

Etotal = (25423.72-14689.3+20339) = 31073.42 N/C

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B)E1 = (0.45*10^-6)/(2*8.85*10^-12) = 25423.72 N/C along -X-axis

E2 = (0.26*10^-6)/(2*8.85*10^-12) = 14689.3 N/C along -X-axis

E3 = (0.36*10^-6)/(2*8.85*10^-12) = 20339 N/C along +X-axis

Etotal at B = E1+E2+E3 = (-25423.72-14689.3+20339) = 19774.02 N/C along left side

C) E1 = (0.45*10^-6)/(2*8.85*10^-12) = 25423.72 N/C along -X-axis

E2 = (0.26*10^-6)/(2*8.85*10^-12) = 14689.3 N/C along +X-axis

E3 = (0.36*10^-6)/(2*8.85*10^-12) = 20339 N/C along +X-axis

Etotal at C = (-25423.72+14689.3+20339) = 9604.6 N/C along right side

D) at D

E1 = (0.45*10^-6)/(2*8.85*10^-12) = 25423.72 N/C along -X-axis

E2 = (0.26*10^-6)/(2*8.85*10^-12) = 14689.3 N/C along +X-axis

E3 = (0.36*10^-6)/(2*8.85*10^-12) = 20339 N/C along -X-axis

Etotal at D = (-25423.72+14689.3-20339) = 31073.41 N/C along left side

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