Three large conducting sheets placed parallel to each other at a finite distance contain charges `Q,-2Q, and 3Q`, respectively. Find the electric fields at points A, B, C, and D.

Explanation

i. Electric field at A is
`vecE_(A) = vecE_1 + vecE_2 + vecE_3`
`vecE_1 harr vecE_2`
`vecE_3 larr`
`:. vecE_1 = Q/(2epsilon_0A) (-hati), vecE_2 = (2Q)/(2epsilon_0A) (hati), and vecE_3 = (3Q)/(2epsilon_0A) (-hati)`
`:. vecE_A = (-Q+2Q-3Q)/(2epsilon_0A) (hati) = Q/(Aepsilon_0) (-hati)`
or `E_A = Q/(Aepsilon_0)` (toward left)
ii. Electric field at B is
`vecE_(B) = vec E_1 + vecE_2 + vecE_3`
`vecE_3 harr vecE_1`
`rarr vecE_2`
`:. vecE_1 = Q/(2epsilon_0A)(hati), vecE_2 = (2Q)/(2epsilon_0A)(hati), and vecE_3 = (3Q)/(2epsilon_0A) (-hati)`
`:. vecE_(B) = (Q + 2Q - 3Q)/(2epsilon_0A) (hati)= 0`
iii. Electric field at C is
`vecE_C = vecE_1 + vecE_2 + vecE_3`
`vecE_2 harr vecE_1` ,brgt `vec E_3 larr `
`:. vecE_1 = Q/(2epsilon_0A)(hati), vecE_2 = (2Q)/(2epsilon_0A)(-hati), and vecE_3 = (3Q)/(2epsilon_0A) (-hati)`
`:. vecE_(C) = (Q - 2Q - 3Q)/(2epsilon_0A) (hati)= (2Q)/(Aepsilon_0) (-hati)`
or `E_C = (2Q)/(Aepsilon_0)` (toward left)
iv. Electric field at D is
`vecE_(D) = vecE_1 + vecE_2 + vecE_3`
`vecE_2 harr vecE_1`
`rarr vecE_3`
`:. vecE_1 = Q/(2epsilon_0A)(hati), vecE_2 = (2Q)/(2epsilon_0A)(-hati), and vecE_3 = (3Q)/(2epsilon_0A) (hati)`
`:. vecE_(D) = (Q - 2Q + 3Q)/(2epsilon_0A) (hati) = Q/(epsilon_0A) (hati)`
or `E_(D) = Q/(Aepsilon_0)` (toward right).