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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Electric Field and Potential

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Field and Potential

Two identical positive charges are positioned at points A and B ....

Two identical positive charges are positioned at points AA and BB. As one travels from AA to BB, the electric potential at locations between AA and BB (excluding the exact locations of the charges)

Options

  1. Ainitially decreases and then increases
  2. Bdecreases continuously
  3. Cincreases continuously
  4. Dinitially increases and then decreases

Correct answer

A. initially decreases and then increases

Step-by-step solution

Let the identical positive charges +q+q be placed at points AA and BB separated by a distance 2a2a.

Let the origin be the midpoint of ABAB. The coordinates of AA and BB are −a-a and +a+a respectively.

The electric potential VV at a distance xx from the midpoint (where −a<x<a-a < x < a) is given by:

V=kqa+x+kqa−x=2kqaa2−x2V = \dfrac{kq}{a+x} + \dfrac{kq}{a-x} = \dfrac{2kqa}{a^2-x^2}

As we move from AA to the midpoint, xx changes from −a-a to 00. The denominator a2−x2a^2-x^2 increases, so VV decreases.

At the midpoint (x=0x=0), VV is minimum.

As we move from the midpoint to BB, xx changes from 00 to aa. The denominator a2−x2a^2-x^2 decreases, so VV increases.

Thus, the electric potential initially decreases and then increases.
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