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NEET PHYSICSELECTROSTATIC POTENTIAL AND CAPACITANCEMedium

Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector P of magnitude, 4×1064\times10^{-6} C m, is ±9×103\pm 9\times10^3 V. (Take 1/4πε0=9×1091/4\pi\varepsilon_0 = 9\times10^9 SI units) Reason (R): V=±2P4πε0r2V = \pm \frac{2P}{4\pi\varepsilon_0 r^2}, where r is the distance of any axial point situated at 2 m from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

A

Both (A) and (R) are True and (R) is not the correct explanation of (A).

B

(A) is True but (R) is False.

C

(A) is False but (R) is True.

D

Both (A) and (R) are True and (R) is the correct explanation of (A).

Step-by-Step Solution

  1. Check Assertion (A): The electric potential VV at an axial point distance rr from a short dipole is given by V=±14πε0Pr2V = \pm \frac{1}{4\pi\varepsilon_0} \frac{P}{r^2}. Given: P=4×106P = 4 \times 10^{-6} Cm, r=2r = 2 m, k=9×109k = 9 \times 10^9 Nm2^2/C2^2. Calculation: V=±(9×109)(4×106)(2)2=±36×1034=±9×103V = \pm \frac{(9 \times 10^9)(4 \times 10^{-6})}{(2)^2} = \pm \frac{36 \times 10^3}{4} = \pm 9 \times 10^3 V. Thus, Assertion (A) is True.

  2. Check Reason (R): The reason statement gives the formula V=±2P4πε0r2V = \pm \frac{2P}{4\pi\varepsilon_0 r^2}. The correct formula for potential is V=P4πε0r2V = \frac{P}{4\pi\varepsilon_0 r^2}. The factor of 2 in the numerator corresponds to the formula for the Electric Field (E=2P4πε0r3E = \frac{2P}{4\pi\varepsilon_0 r^3}) or is simply incorrect for potential. Thus, Reason (R) is False.

  3. Conclusion: (A) is True but (R) is False.

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 CAPACITANCEstatementslabelledassertionlabelledreason

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