Three charges q,q and -2q are placed at the 3 vertices of an equilateral triangle. Then what is the equivalent dipole moment of the system
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The equivalent dipole moment of the system is D.M= 3 / √2 qdi + ( 1 - √2 / √ 2 ) qdj
Explanation:
Since this system of charges is a non-neutral system.
Dipole momentum of system
- 2q (d / √ 2 ) ( - j) + ( - 2q ) (d / √ 2 ) ( -i) + q (d / √ 2 ) + q (d / √ 2 ) (- j )+ (-q)dj
= √2 qdj + √2 qdi + 1/ √2 qdi - 1/ √ 2 qdj = qdj
= 3 / √ 2 qdi + qdj ( √2 - 1 /√2 - 1 )
= 3 / √2 qdi + ( 1 - √2 / √ 2 ) qdj
The electric potential energy of a system of three point charges can be calculated in a similar manner
U = 1 / 4πεo ( q1q2 / r12 + q1q3 / r13 + q2q3 / r23)
Thus the equivalent dipole moment of the system is D.M= 3 / √2 qdi + ( 1 - √2 / √ 2 ) qdj
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