Back to Directory
NEET PHYSICSMedium

Three point charges +q, -2q and +q are placed at points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:

A

√2qa along +y direction

B

√2qa along the line joining points (0, 0, 0) and (a, a, 0)

C

qa along the line joining points (0, 0, 0) and (a, a, 0)

D

√2qa along +x direction

Step-by-Step Solution

The system can be treated as the superposition of two electric dipoles. The charge -2q at the origin (0,0,0) can be split into two charges of -q.

  1. Dipole 1: Formed by -q at (0,0,0) and +q at (a,0,0). The dipole moment vector p⃗1\vec{p}_1 points from negative to positive charge, i.e., along the +x axis. Magnitude p1=q×ap_1 = q \times a. So, p⃗1=qai^\vec{p}_1 = qa \hat{i}.
  2. Dipole 2: Formed by the remaining -q at (0,0,0) and +q at (0,a,0). The dipole moment vector p⃗2\vec{p}_2 points along the +y axis. Magnitude p2=q×ap_2 = q \times a. So, p⃗2=qaj^\vec{p}_2 = qa \hat{j}.
  3. Resultant Dipole Moment: p⃗net=p⃗1+p⃗2=qa(i^+j^)\vec{p}_{net} = \vec{p}_1 + \vec{p}_2 = qa(\hat{i} + \hat{j}).
  4. Magnitude: ∣p⃗net∣=(qa)2+(qa)2=2qa|\vec{p}_{net}| = \sqrt{(qa)^2 + (qa)^2} = \sqrt{2}qa.
  5. Direction: The vector i^+j^\hat{i} + \hat{j} lies in the xy-plane at 45° to the x-axis, which corresponds to the line joining the origin (0,0,0) and the point (a,a,0).
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started
Solved: PHYSICS Question for NEET | Sushrut