Question:
use gauss law to drive the expression for electric field between 2 uniformly charge parallel sheets with surface charge density sigma and sigma respectively
Answer:
Electric field of two positively charged parallel sheets-
The figure shows two thin plane parallel sheets of charge having uniform charge densities σ1 and σ2 .
r^ is a unit vector pointing from left to right.
E1 is the electric field due to sheet 1 and E2 is field due to sheet 2.
We have three regions here, left from the sheets - Region I
Between the sheets - Region II
Right from sheets- Region III
So, in the Region I : Fields due to the two sheets are-
E1 = -(σ1 /2ε0 )r^ , E2 = -(σ2 /2ε0 )r^
So, total electric field in this region = EI = E1+ E2 = -r^/2ε0 (σ1+σ2)
In Region II :
E1 = (σ1 /2ε0 )r^ , E2 = -(σ2 /2ε0 )r^
Total field, EII = E1+ E2 = r^/2ε0 (σ1-σ2)
In Region III :
E1 = (σ1 /2ε0 )r^ , E2 =(σ2 /2ε0 )r^
total electric field in this region = EIII = E1+ E2 = r^/2ε0 (σ1+σ2)
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