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Derive an expression for the electric field at any point along the axial line of an electrical dipole. |
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Answer» Solution :The electric field at a point P on axial line of dipole due to +q charge B. ` E_B =(1)/(4 pi in _0).(q)/((R-a)^(2)) ` along BP and electric field due to -q charge at A is ` "" E_A =(1)/(4 pi in _0).(q)/( (r+a) ^(2)) ` along PB ` therefore` Net electric field at point P is GIVEN by ` E= E_B -E_A =(q)/(4 pi in_0)[(1)/((r-a)^(2) )-( 1)/((r+a)^(2)) ]= (q. 4ar)/(4pi in _0(r^(2) -a^(2) )^(2)) ` `rArr "" E= (2pr)/(4 pi in _0(r^(2) -a^(2))^(2)) , `where p=q ,2a=dipole moment of given dipole. For a short dipole or if the point P is situated far away, then a `ltlt ` r and hence, ` ""E =(1)/(4piin _0) .(2p)/(r^(3)) `along ABP Vectorially ` oversetto E= (1)/(4 pi in _0).(oversetto 2p)/(r^(3)) ` 
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