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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
The Forces

Concepts Of Physics MCQ Edition [Volume 1] · Physics · The Forces

Determine the distance at which two charges, each equal to 1 C ,...

Determine the distance at which two charges, each equal to 1 C1 \text{ C}, must be placed so that the force between them is equal to your weight WW.

Options

  1. A14πε0W\sqrt{\dfrac{1}{4\pi\varepsilon_0 W}}
  2. B14πε0W\dfrac{1}{4\pi\varepsilon_0 W}
  3. C14πε0W\dfrac{1}{4\pi\varepsilon_0 \sqrt{W}}
  4. D4πε0W\sqrt{\dfrac{4\pi\varepsilon_0}{W}}

Correct answer

A. 14πε0W\sqrt{\dfrac{1}{4\pi\varepsilon_0 W}}

Step-by-step solution

According to Coulomb's law, the electrostatic force between two charges q1q_1 and q2q_2 separated by a distance rr is given by F=14πε0q1q2r2F = \dfrac{1}{4\pi\varepsilon_0} \dfrac{q_1 q_2}{r^2}.

Given that q1=1 Cq_1 = 1 \text{ C}, q2=1 Cq_2 = 1 \text{ C}, and F=WF = W.

Substituting these values into the formula, we get W=14πε01×1r2W = \dfrac{1}{4\pi\varepsilon_0} \dfrac{1 \times 1}{r^2}.

Rearranging the equation to solve for r2r^2, we obtain r2=14πε0Wr^2 = \dfrac{1}{4\pi\varepsilon_0 W}.

Taking the square root of both sides gives r=14πε0Wr = \sqrt{\dfrac{1}{4\pi\varepsilon_0 W}}.
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