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Define electric dipole moment. Is it a scalar or a vector ? Derive the expression for the electric field of a dipole at a point on the equatorial line of the dipole. |
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Answer» Solution :For definition of dipole moment, see point Number 29 under the heading "Chapter At a Glance"Dipole moment is a vector. LET us calculate the electrostatic field at a point P on the equatorial line at a DISTANCE .r. form mid- point O of an electric dipole AB. Obviously, `""|oversetto (E_A) |=|oversetto (E_B)| =(1)/(4 pi in _0).(q)/( (a^(2) + r^(2))) ` Resultant field at POINTP is `oversetto E =oversetto (E_A) +oversetto (E_B) ` Let us RESOLVE ` oversetto (E_A) and oversetto (E_B) ` along and perpendicular to the dipole axis. We find that components `E_A sin theta and E_B sin theta ` nullify each other and hence ` |oversetto E| =(oversetto (E_A) +oversetto (E_B)) cos theta =2 .(1)/(4 pi in _0) .(q)/((a^(2) + r^(2)) ).(a)/(sqrt(a^(2) +r^(2)) ) ` where p=q.2a =dipole moment of electric dipole This DIRECTION of ` oversetto E ` is opposite to that of ` oversetto p i.e. , oversetto E =-(oversetto p)/( 4 pi in _0( r^(2) +a^(2)) ^(3//2)) ` If` r gt gt a , `then teh above relation may be modified as ` "" oversetto E =-(oversetto p)/( 4 pi in _0 r^(3)) ` ` (##U_LIK_SP_PHY_XII_C01_E10_002_S01.png" width="80%"> |
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