Chapter 22 A point charge +2Q is at the origin and a point charge -Q is located along the x axis at x = d as in the figure below. Find a symbolic expression for the net force onalong the y axis at y = d. (Use the following as necessary: ke, the Coulomb constant, Q, and d.)third point charge +Q locatedFnet =+Q+2Qd-Q

Name: Chapter 22 A point charge +2Q is at the origin and a point charge -Q i
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Description: Chapter 22 A point charge +2Q is at the origin and a point charge -Q is located along the x axis at x = d as in the figure below. Find a symbolic expression for the net force onalong the y axis at y = d. (Use the following as necessary: ke, the Coulo

Answered: A point charge +2Q is at the origin and…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Chapter 22

A point charge +2Q is at the origin and a point charge -Q is located along the x axis at x = d as in the figure below. Find a symbolic expression for the net force on
along the y axis at y = d. (Use the following as necessary: ke, the Coulomb constant, Q, and d.)
third point charge +Q located
F
net =
+Q
+2Q
d
-Q

Expert Solution

Step 1 Forces between charges

The force between two charges can be calculated using the Coulomb's law ,

F = $K_{e} \frac{Q_{1} Q_{2}}{r^{2}}$

Let F₁ be the force exerted by charge +2Q at origin on charge +Q at y =d ,

F₁ = $K_{e} \frac{(2 Q) (Q)}{d^{2}}$ $\overset{⏞}{j}$ , F₁ = $\frac{2 K_{e} Q^{2}}{d^{2}}$ $\hat{j}$

let F₂ be the force exerted by the charge -Q at x = d on charge +Q at y =d

Since the distance of both the charges is same from origin , it makes an isosceles triangle ,

Hence ,

F_2x = $K_{e} \frac{(- Q) (Q)}{{(\sqrt{2} d)}^{2}} \cos (45 °) \hat{i}$

$F_{2 x} = \frac{- K_{e} Q^{2}}{2 d^{2}} x \frac{\sqrt{2}}{2} \hat{i}$

F_2x = $- \frac{K_{e} Q^{2}}{2 \sqrt{2}} \hat{i}$ ,

Similarly , F_2y = $- \frac{K_{e} Q^{2}}{2 \sqrt{2}} \hat{j}$

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