Answered: A 15.5 mC charge is fixed at the origin…

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

A 15.5 mC charge is fixed at the origin in the xy plane, and a -22.2 mC charge is fixed at (x,y) = (3.00, 0)
meters. Find the electric field at point A at (x,y) = (0, 4.00) m in column vector notation. If an electron is
placed at (0, 4.00) m, what would be the force on it?

Expert Solution

Step 1: Electric field at A

$Due space to space 15.5 space mC straight E subscript 1 equals fraction numerator straight K left parenthesis 15.5 space mC right parenthesis over denominator 4 squared end fraction straight j with hat on top space space equals fraction numerator 9 cross times 10 to the power of 9 left parenthesis 15.5 cross times 10 to the power of negative 3 space end exponent straight C right parenthesis over denominator 4 squared end fraction straight j with hat on top space space equals stretchy left parenthesis 8.72 cross times 10 to the power of 6 space C stretchy right parenthesis bold space bold j with bold hat on top Due space to space minus 22.2 space mC straight E subscript 2 equals fraction numerator 9 cross times 10 to the power of 9 cross times 22.2 cross times 10 to the power of negative 3 end exponent over denominator 5 squared end fraction sin left parenthesis 36.87 to the power of straight o right parenthesis space straight i with hat on top minus fraction numerator 9 cross times 10 to the power of 9 cross times 22.2 cross times 10 to the power of negative 3 end exponent over denominator 5 squared end fraction cos left parenthesis 36.87 to the power of straight o right parenthesis space straight j with hat on top space space space space space space space space space space space space space space space space space left parenthesis see space diagram right parenthesis space space equals stretchy left parenthesis 4.80 cross times 10 to the power of 6 stretchy right parenthesis bold space bold i with bold hat on top bold minus bold left parenthesis bold 6 bold. bold 39 bold cross times bold 10 to the power of bold 6 bold right parenthesis bold space bold j with bold hat on top Total space electric space field space is straight E equals straight E subscript 1 plus straight E subscript 2 space space equals stretchy left parenthesis 4.80 cross times 10 to the power of 6 stretchy right parenthesis space straight i with hat on top plus left parenthesis 8.72 cross times 10 to the power of 6 minus 6.39 cross times 10 to the power of 6 right parenthesis space straight j with hat on top space space space equals stretchy left parenthesis 4.80 cross times 10 to the power of 6 stretchy right parenthesis space straight i with hat on top plus left parenthesis 2.33 cross times 10 to the power of 6 right parenthesis space straight j with hat on top space column space vector space is bold E bold equals stretchy left parenthesis table row cell stretchy left parenthesis 4.80 cross times 10 to the power of 6 stretchy right parenthesis end cell row cell left parenthesis 2.33 cross times 10 to the power of 6 right parenthesis end cell end table stretchy right parenthesis$

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