Three charges are at the corners of an equilateral triangle, as shown in the figure below. Calculate the electric field at a pointmidway between the two charges on the x-axis. (Let q, = 9.00 µC, q, = 7.50 µC, and q3 = -2.00 µC.)+0.500 m60.0°

we have following data as given in above question q1 = 9.00 uC = 9×10-6 C q2 = 7.50 uC = 7.5×10-6 C…

Answered: Three charges are at the corners of an…

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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Question

Three charges are at the corners of an equilateral triangle, as shown in the figure below. Calculate the electric field at a point
midway between the two charges on the x-axis. (Let q, = 9.00 µC, q, = 7.50 µC, and q3 = -2.00 µC.)
+
0.500 m
60.0°

Expert Solution

Step 1

we have following data as given in above question

$q_{1} = 9.00 uC = 9 \times 10^{- 6} C$

$q_{2} = 7.50 uC = 7.5 \times 10^{- 6} C$

$q_{3} = - 2.00 uC = - 2 \times 10^{- 6} C$

side of equilateral triangle is 0.5 m.

As you are observing in figure below we have to calculate electric field at point midway between the two charges at point D the electric field due to charge q₁ at point D will be in negative direction of y-axis, the electric field due to charge q₂ at point D will be in positive direction of x-axis and the electric field due to charge q₃ will be in positive direction of x-axis

as you are observing that $∆ ABD$ is right angle triangle then the value of BD will be written as

$BD = \sqrt{{AB}^{2} - {AD}^{2}}$

$BD = \sqrt{0 . 5^{2} - 0 . 25^{2}}$

$BD = \sqrt{0.1875}$

$BD = 0.43 m$

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