Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform
ID: 1576399 • Letter: T
Question
Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities S1, S2, Sa, and S4 on their surfaces (Fig. E22.30). These surface charge densities have the values 1--6.00 C/m", 2 = +5.00 0/m2,03 = +2.00 C/m", and 4 = +4.00 C/m2. Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets: (a) point A, 5.00 cm from the left face of the left-hand sheet, (b) point B, 1.25 cm from the inner surface of the right-hand sheet; (c) point C, in the middle of the right-hand sheet. Figure E22.30 10 cm 12 cm 10 cmExplanation / Answer
As the sheets are very large as compared to other dimensions, the distance of points A, B and C from sheets do not matter for calculation of electric field.
For any point the sum of left charge densities will provide one electric field. And similarly sum of all the right charge densities will provide another electric field. The net electric field will be vecor sum of these two.
For A:
No charge density in the left. And sum of all the right charge densities
R = 1+2+3+4
R = -6+5+2+4
R = +5 C/m2
Electric field at A, EA = R/20
EA = 0.5 x (5 x 10-6)/(8.85 x 10-12)
EA = 0.28248 x 106 N/C
EA = 282.48 kN/C towards left
For B:
Sum of all the left charge densities
L = 1+2
L = -1 C/m2
Electric field at B due to left charge densities,
EBL = L/20
EBL = 56.5 kN/C towards left
Similarly
R = 3+4
R = 6 C/m2
Electric field at B due to left charge densities,
EBR = R/20
EBR = 338.97 kN/C towards left
Net electric field at B
EB = EBL + EBR (to be added vectorially)
EB = 395.75 kN/C towards left
For C:
L = 1 C/m2
R = 4 C/m2
ECL = 56.5 kN/C towards right
ECR = 226 kN/C towards left
Net electric field at C
EC = ECL + ECR (to be added vectorially)
EC = 169.5 kN/C towards left
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