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On the x-y plane to point charges +q and -q are placed at positiions (0,l) and (0,-l) respectively. Find an expression for the intensity of electric field at a point (0,y) where ygtl. Under what condition does the charge system bechave as a dipole and hence express the electric field in terms of the dipole moment of the dipole so formed. |
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Answer» SOLUTION :Suppose, electric field intensity at the point C due to the charges A and B are `E_(1)` and `E_(2)`, RESPECTIVELY. `:.E_(1)=1/(4 pi epsilon_(0)) .q/((y-l)^(2))`, along `vec(CY)` `E_(2)=1/(4 pi epsilon_(0)) . q/((y+l)^(2))`, along `vec(CA)`  As `E_(1)` and `E_(2)` are acting the opposite directions and `E_(1)gtE_(2)`, the RESULTANT electric field at C is `E=E_(1)-E_(2)` `=1/(4 pi epsilon_(0)) . q.((y-l)^(2)) - 1/(4 pi epsilon_(0)) . q/((y+l)^(2))` `=q/( 4 pi epsilon_(0)) [ 1/((y-l)^(2)) - 1/ ((y+l)^(2))] = q/(4 pi epsilon_(0)) . (4yl)/((y^(2)-l^(2))^(2))` `=1/(4 pi epsilon_(0)) . (4qyl)/(y^(4)) [ :' y gtl]` `=1/(4pi epsilon_(0)) . (4ql)/(y^(3))`, along `vec(CY)` If the value of l issmall, the COMBINATION of the charges behave as an electric dipole with dipole moment, `p=qxx2l`. In that case `E=1/(4 pi epsilon_(0)) . (2p)/(y^(3))`, along `vec(CY)` |
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