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Two large charged plane sheets of charge densities sigma and - 2sigma C//m^(2)are arranged vertically a separation of d between them. Deduce expressions for the electric field at pointsto the left of the first sheet , (ii) To right of the second sheet, between the two sheets. |
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Answer» Solution :Consider TWO large charged plane sheets of surface charges DENSITIES `+sigma and -2 sigma ` arranged vertically with a separation .d. between them. At any point `P_1` left of first sheet ,electric field due to the two sheets are `E_1 =(sigma)/( 2 in _0)and E_2 (2sigma )/(2 in _0)=(sigma )/( in_0) ` and their DIRECTIONS are MUTUALLY opposite as shown here . ` therefore ` Net electric fieldat ` P_1 , E=E_2-E_1=(sigma )/(in_0)-(sigma )/( 2 in _0)=(sigma )/( 2 in _0) ` towards the first sheet. (ii) At any point ` P_2` right of second sheet `E_1 =(sigma )/( 2 in _0)and E_2 =(sigma )/( in_0)` and their directions are again mutually opposite as shown ` therefore ` Net electric field at `P_2 ,E =E_2 -E_1 =(sigma )/( in_0)-(sigma)/( 2 in _0)=(sigma)/ (2 in _0)` towards the second sheet. (iii) At a point `P_3` between the two sheets both ` E_1and E_2` are DIRECTED in same directions . Hence net electric field at ` P_3 , E= E_1+E_2 =(sigma)/( 2 in _0)+(sigma)/(in_0)=(3 sigma )/( 2 in _0)` towards the second sheet. 
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