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NEET PHYSICSELECTROSTATIC POTENTIAL AND CAPACITANCEMedium

Question

Charges +q+q and −q-q are placed at points A and B, respectively, which are at a distance 2L2L apart. C is the midpoint between A and B. The work done in moving a charge +Q+Q along the semicircle CRD is:

A

qQ4πϵ0L\frac{qQ}{4\pi\epsilon_0 L}

B

qQ2πϵ0L\frac{qQ}{2\pi\epsilon_0 L}

C

qQ6πϵ0L\frac{qQ}{6\pi\epsilon_0 L}

D

−qQ6πϵ0L-\frac{qQ}{6\pi\epsilon_0 L}

Step-by-Step Solution

  1. Conservative Nature: The work done by the electrostatic force is independent of the path taken and depends only on the potential difference between the final and initial points [NCERT Class 12, Sec 2.1]. Thus, the work done moving charge QQ from C to D is W=Q(VD−VC)W = Q(V_D - V_C).
  2. Potential at C (Midpoint): Point C is equidistant (LL) from +q+q and −q-q. The potential VCV_C is the sum of potentials due to individual charges: VC=14πϵ0(+qL+−qL)=0V_C = \frac{1}{4\pi\epsilon_0} \left( \frac{+q}{L} + \frac{-q}{L} \right) = 0
  3. Location of D: While the diagram is not provided, the options and the nature of the problem (AIPMT 2007) imply that D is a point on the axis of the dipole, situated at distance LL from B (outside the dipole). Thus, the distance from +q+q (at A) is 3L3L and from −q-q (at B) is LL.
  4. Potential at D: VD=14πϵ0(+q3L+−qL)=q4πϵ0L(13−1)=q4πϵ0L(−23)=−q6πϵ0LV_D = \frac{1}{4\pi\epsilon_0} \left( \frac{+q}{3L} + \frac{-q}{L} \right) = \frac{q}{4\pi\epsilon_0 L} \left( \frac{1}{3} - 1 \right) = \frac{q}{4\pi\epsilon_0 L} \left( -\frac{2}{3} \right) = -\frac{q}{6\pi\epsilon_0 L}
  5. Work Done: W=Q(VD−VC)=Q(−q6πϵ0L−0)=−qQ6πϵ0LW = Q(V_D - V_C) = Q \left( -\frac{q}{6\pi\epsilon_0 L} - 0 \right) = -\frac{qQ}{6\pi\epsilon_0 L}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from ELECTROSTATIC POTENTIAL AND CAPACITANCE. 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.

PHYSICSELECTROSTATIC POTENTIAL AND CAPACITANCEchargesplacedpointsrespectivelydistance

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