## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson

# Chapter 25 - Electric Charges and Forces - Exercises and Problems: 39

#### Answer

The force on the +1.0 nC charge is $1.0\times 10^{-3}~N$ directed to the left.

#### Work Step by Step

We can find the distance $r$ from the +1.0 nC charge to each of the other charges. $r = \sqrt{(0.5~cm)^2+(0.5~cm)^2}$ $r = 0.71~cm$ By symmetry, the vertical component of each force on the +1.0 nC charge cancels out. The net force on the +1.0 nC charge is the sum of the horizontal component of each force. The horizontal component of each force on the +1.0 nC charge is directed to the left. $F = 4\times \frac{(k)(1.0~nC)(2.0~nC)}{r^2}~cos(45^{\circ})$ $F = 4\times \frac{(9.0\times 10^9~N~m^2/C^2)(1.0\times 10^{-9}~C)(2.0\times 10^{-9}~C)}{(0.0071~m)^2}~cos(45^{\circ})$ $F = 1.0\times 10^{-3}~N$ The force on the +1.0 nC charge is $1.0\times 10^{-3}~N$ directed to the left.

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