Three short electric dipoles, each of dipole moment P, are placed at the vertices of an equilateral triangle of side length L. Each dipole has its moment, oriented parallel to the opposite side of the triangle as shown in the fig. The electric field strength at the centroid of the triangle is √a(K P/L3). Then value of a is:

Question

Three short electric dipoles, each of dipole moment P, are placed at the vertices of an equilateral triangle of side length L. Each dipole has its moment, oriented parallel to the opposite side of the triangle as shown in the fig. The electric field strength at the centroid of the triangle is √a(K P/L3). Then value of a is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-jb7bqvtkjlpnwy9o.jpg" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-jb7bqvtkjlpnpylk.jpg" /> From superposition E=((2 K P/r3)) opposite to 2 overset arrow P =(2 K P/((L)√3)3) r=(2/3)× (√3 L/2)=(L/√3) =6√3((K P/L3)) ∴ a=108

From superposition E=(r32KP​) opposite to 2P→ =(3​L​)32KP​ r=32​×23​L​=3​L​ =63​(L3KP​) ∴a=108

From superposition
$E = (\frac{2 K P}{r ^{3}})$ opposite to $2 P \to$
$= \frac{2 K P}{( \frac{L}{3} ) ^{3}}$ $r = \frac{2}{3} \times \frac{3 L}{2} = \frac{L}{3}$
$= 63 (\frac{K P}{L ^{3}})$
$∴ a = 108$