Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the magnitude of dipole moment of the combination.

Question

Three charges are arranged on the vertices of an equilateral triangle as shown in figure- Find the dipole moment of the combination-

Toppr Admin · Accepted Answer

Let -x2212-q -amp- -x2212-q are placed at A -amp- CWhere 2q on BSo length of A-dSo the dipole moment-xA0-p-q-xD7-d-So- Resultant dipole momentP-qd-2-qd-2-2qd-xD7-qdcos60o-1-2-3q2d2-1-2-x221A-3qd-x221A-3P-

Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.

Let $- q$ & $- q$ are placed at A & C
Where $2 q$ on B
So length of $A = d$

So the dipole moment
$p = (q \times d)$

So, Resultant dipole moment
$P = [(q d)^{2} + (q d)^{2} + 2 q d \times q d cos 60^{o}]^{1 / 2}$

$= [3 q^{2} d^{2}]^{1 / 2} = \sqrt{3} q d = \sqrt{3} P$ .

Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.

Let −q & −q are placed at A & CWhere 2q on BSo length of A=dSo the dipole moment p=(q×d)So, Resultant dipole momentP=[(qd)2+(qd)2+2qd×qdcos60o]1/2=[3q2d2]1/2=√3qd=√3P.

Let $- q$ & $- q$ are placed at A & C
Where $2 q$ on B
So length of $A = d$

So the dipole moment
$p = (q \times d)$

So, Resultant dipole moment
$P = [(q d)^{2} + (q d)^{2} + 2 q d \times q d cos 60^{o}]^{1 / 2}$

$= [3 q^{2} d^{2}]^{1 / 2} = \sqrt{3} q d = \sqrt{3} P$ .