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NEET PHYSICSELECTRIC CHARGES AND FIELDSMedium

Question

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 p1\vec{p}_1 points from negative to positive charge, i.e., along the +x axis. Magnitude p1=q×ap_1 = q \times a. So, p1=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 p2\vec{p}_2 points along the +y axis. Magnitude p2=q×ap_2 = q \times a. So, p2=qaj^\vec{p}_2 = qa \hat{j}.
  3. Resultant Dipole Moment: pnet=p1+p2=qa(i^+j^)\vec{p}_{net} = \vec{p}_1 + \vec{p}_2 = qa(\hat{i} + \hat{j}).
  4. Magnitude: pnet=(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).

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from ELECTRIC CHARGES AND FIELDS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSELECTRIC CHARGES AND FIELDSchargesplacedpointsrespectivelymagnitude

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