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charges q,q,-2q are placed at the corners of equilateral triangle of side l. what is the net dipole moment? Ans root3 ql. pl explain

charges q,q,-2q are placed at the corners of equilateral triangle of side l. what is the net dipole moment?


Ans root3 ql.


pl explain

Grade:

5 Answers

vikas askiitian expert
509 Points
10 years ago

let A,B,C are three vertices ...

charge at A,B is q but at C charge is -2q ...

A(q) ...................B(q)

 

 

           C(-2q)

 

charge of C can be written as -q + -q

q charge of A & -q charge of C becomes 1 dipole ...

q charge of B & another -q charge of C makes another dipole ..

direction of dipole moments of  both is rowards C .....

angle bw them will be 60o ...

now resultant = root(p2+p2+2p2cos60o) = root3 (P)

now , P = qL so resultant = root3(qL)

anu gupta
20 Points
8 years ago

the answer of the question :the resultant dipole moment of 3 charges placed at the vertices of the triangle is root3qL or -root3 qL

Arpit
11 Points
5 years ago
Explanation given by vikas is correct.
Except that “Direction of dipole is from negative to positive.” then only its answer will “root(3)ql”.
Otherwise if “direction of dipole moments of  both is towards C …..” it will be in negative j-direction,since it is a vector quantity.
Therefore answer will become “-root3(ql)”
Y
/\
|   A(Q)-------------------B(Q)
|
|
|
|             C(-2Q)
|
|----------------------------------->X
Pran
11 Points
4 years ago
Dipole is only an applicable condition when and only when the charges are also equal in magnitude rather than only being opposite.So, 1st we break -2q charge at C as -q +(-q).Now there are 2 -q charges at C i.e. 1 to complete dipole with A and another with B.Now,Dipole due AC=dipole due BC = q.aSo net dipole = vector sum dipole due AC and due BC where angle b\w the 2 vectors =60°So net dipole=√(qa)²+(qa)²+2qacos60° =√3qa
Yash Chourasiya
askIITians Faculty 256 Points
11 months ago
Dear Student

Consider an equilateral triangle of side l. Point A and B have charges +q where A has -2q charge. The system as two dipoles with P1 and P2 along BA and CA respectively. Hence, the magnitude of P1 and P2 are equal to (ql) and the angle between them is 60°. Therefore, the resultant of two is the net dipole moment.643-1148_Untitled.png
Now resultant = √(p2+p2+2p2cos60o) = (P)√3

now , P = qL
so resultant = qL√3

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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