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Question

Determine the electric dipole moment of the system of three charges,placed on the vertices of an equilateral triangle ,as shown in the figure:
1333326_b13730933efa41b68c02d31f0991ca5a.png

A
(ql)^i+^j2
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B
3ql^j^i2
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C
3ql^j
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D
2ql^j
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Solution

The correct option is C 3ql^j
Step 1:Breaking the Charge -2q
Make the dipoles out of the given system of charges by breaking up charge 2q as q and q as shown in Figure
Step 2: Dipole moments of the dipole formed
We know that the direction of a dipole is from q to q.
Now we have two dipole vectors P1 and P2 as shown in Figure.
Magnitude of dipoles: P1=ql, P2=ql
P1=P2=P=ql

Step 3: Resultant dipole moment
As sine components of P1 and P2 would cancel each other.
Net dipole moment =Pcos30o(^j)+Pcos30o(^j)
=2qlcos30o^j=3ql^j
Hence, Option (C) is correct.

2110657_1333326_ans_1712de9ee2024ff4bb720717426736c3.png

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