Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surf
ID: 2283735 • Letter: T
Question
Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of -9.60?C/m2 , and sheet B, which is to the right of A, carries a uniform charge of -11.4?C/m2 . Assume the sheets are large enough to be treated as infinite.
A)Find the magnitude of the net electric field these sheets produce at a point 4.00 cm to the right of sheet A.
B) Find the direction of the net electric field these sheets produce at a point 4.00 cm to the right of sheet A.
C) Find the magnitude of the net electric field these sheets produce at a point 4.00 cm to the left of sheet A.
D )Find the direction of the net electric field these sheets produce at a point 4.00 cm to the right of sheet A.
E)Find the magnitude of the net electric field these sheets produce at a point 4.00 cm to the right of sheet B.
F) Find the direction of the net electric field these sheets produce at a point 4.00 cm to the right of sheet B.
Explanation / Answer
If these parallel sheets are very large we can assume that electric fields between the sheets are spatially uniform. This type of problem can be best solved by using superposition.
a) Let P1 be the point 4 cm to the right of sheet A. The electric fields at P1 are due to the charge sheets A and B. But since P1 is placed right between sheet A and B, these electric fields are in the opposite direction. So E_net = E_A - E_B
Electric field due to an infinitely large sheet of charge = ? / ?
E_A = -9.4 * 10^-6 C/m^2 / (8.85*10^-12 F/m) = -1.06*10^6 N/C
E_B = -11.1 * 10^-6 C/m^2 / (8.85*10^-12 F/m) = -1.25*10^6 N/C
E_net = 1.90 * 10^5 N/C
b) Let P2 be the point 4 cm to the left of sheet A. Now P2 is to the left of both sheets A and B. Electric fields due to sheets A and B will add up.
E_net = -(E_A + E_B)
The minus sign there is because P2 is left of both sheets.
E_net = 2.31 * 10^6 N/C
c) Let P3 be the point 4 cm to the right of sheet B. Electric fields due to sheets A and B will add up.
E_net = E_A + E_B
The reason there is no minus sign this time is because P3 is right to both sheets.
= -2.31 * 10^6 N/C
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