Answered: Three, equal, positive, point charges…

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter9: Condensed Matter Physics

Section: Chapter Questions

Problem 58P: The measured density of a CsCl crystal is 3.988 g/cm3. What is the equilibrium separate distance of...

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Three, equal, positive, point charges are moved through a uniform electric field as shown in the diagram below. Let W₁, W₂, and W₃ equal the amount of work done by the electric field on charges q₁, q₂, and q₃ respectively. Which of the following statements is true?

W₃ < W₂ < W₁

W₂ > W₃ > W₁

W₁ = W₂ = W₃

W₁< W₂< W₃

W₁ > W₃ > W₂

Expert Solution

Step 1

Given information :-

Uniform electric field $\vec{E}$

Three equal positive point charges $q_{1} = q_{2} = q_{3} = q (l e t)$

Explanation :-

If we look the given graph carefully, we notice that all the three charges move a distance d = 3 m (= 5 m - 2 m) along the direction of electric field.

Note :- Here it seems that charge $q_{3}$ moves larger distance (see the curve along which the $q_{3}$ moves) in the region of electric field but in the formula $E = \frac{∆ V}{d}$ , d is the projection of the distance between two points along the electric field, $E$ is the electric field and $∆ V$ is the potential difference between those two points. So the distance moved by charge $q_{3}$ is same as the distance moved by the charge $q_{1}$ . By the same token we can say that distance moved by charge $q_{2}$ is same as the distance moved by the other two charges $q_{1} a n d q_{3}$ . This distance d is along electric field and its value is d = 3 m(same for all the three charges).

Again we know that work done W in moving a charge q between two points in an electric field $E$ is given by

$W = q . ∆ V$

$W = q . E . d (∴ E = \frac{∆ V}{d}) . . . . . . . . . . . . . . . . . . . . . 1$

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