Three very large sheets are separated by equal distances of 20.0 cm(see the figu

Question

Three very large sheets are separated by equal distances of 20.0 cm(see the figure). The first and third sheets are very thin andnonconducting and have charge per unit area ? of+3.50C/m2 and -3.50C/m2, respectively. The middle sheet isconducting but has no net charge. (a) What is the electric field inside themiddle sheet? 1 N/C 2 (b) What is the electric field between the left and middlesheets? 3 N/C 4 (c) What is the electric field between the middle and rightsheets? 5 N/C 6 (d) What is the charge density on the surface of the middle sheetfacing the left sheet? 7 C/m^2 (e) What is the charge density on the surface of the middle sheetfacing the right sheet? 8 C/m^2

Explanation / Answer

a) there is no field inside the middle conducting sheetbecause if there were    a field current would flow. b&c) The electric field due to a large nonconducting sheetis      E = /(20) by Gauss' Law = Q /0 = A/0 = 2 E A      since field lines pass only thru theends of a Gaussian "pillbox"      drawn thru the non-conductingsheet - note that the field does not      depend on the distance from thesheet because no lines of flux pass      thru the sides of the pillbox d&e) from the above analysis the charge density on eitherside of the middle      conducting sheet must 1/2 ofthat on the non-conducting sheet or /2 and      be opposite in sign to the sheetfacing the middle sheet      (Physically the charge on thenon-conductor is /2 on each side of the sheet       and induces /2 on theopposite conductor)   

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