1.

four charge +q ,-2q,+q,-q are place at four vertex of square of side a find the potential at the centre of the square

Answer»

Electric field at P due to charge at A is,EA= kq/(a2/2) along APElectric field at P due to charge at B is,EB= k(2q)/(a2/2) along BPElectric field at P due to charge at C is,EC= k(3q)/(a2/2) along CPElectric field at P due to charge at D is,ED= k(4q)/(a2/2) along DPElectric field EAand ECare in opposite directions, so, their net field is,ECA= k(3q)/(a2/2) - kq/(a2/2) = k(2q)/(a2/2) along CAElectric field EDand EBare in opposite directions, so, their net field is,EDB= k(4q)/(a2/2) - k(2q)/(a2/2) = k(2q)/(a2/2) along DBSince, ECAand EDBare equal in magnitude and they are perpendicular to each other, so, their resultant E will bisect angle APB.Thus, E = [(ECA)2+ (EDB)2]1/2= (√2)k(2q)/(a2/2) = (4√2)kq/a2



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