Three point charges of +2q, -q and -q are placed at the corners A, B and C of an equilateral triangle ABC of side ‘x’. What is the magnitude of the electric dipole moment of this system?

1 Answer
P dilip_k
Sep 23, 2017

The center of charge of two point charges each of magnitude -q placed at B and C will be at the mid point of BC . Let this point be D. The effective charge at B will be -2q.

So the dipole system will be due to positioning of two point charges of magnitude #+2q# at A and #-2q# at D. The distance AD is the height of the equilateral triangle ABC of side #x#.

So #AD=sqrt3/2x#

Hence the dipole moment of the system #=2qxxsqrt3/3x=sqrt3qx#

Alternative way

The system may also be considered as composed of two dipoles 'AC' and 'BC' each having moment of magnitude #p=qx# and they are aligned at an angle #theta =60^@#

So resultant dipole moment will be

#p_"reultant"=sqrt(p^2+p^2+2p^2cos60^@)=sqrt3p=sqrt3qx#

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