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

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 26 - The Electric Field - Exercises and Problems - Page 777: 47

Answer

$1.41\times 10^5\;{\rm N/C}\;\hat i $

Work Step by Step

As we can see from the figure below, the net electric field from both spheres is in the right direction. And since the point between the two spheres is greater than their radius, the electric field of the sphere appears as an electric field of a point charge. Thus, $$E_{net}=(E_1+E_2)\hat i=\left[\dfrac{kq_1}{r_1^2}+\dfrac{kq_2}{r_2^2}\right]\hat i$$ where $r_1=r_2=3+1=4$ cm. $$E_{net} =\left[ \dfrac{(9\times 10^9)(10\times 10^{-9})}{0.04^2}+\dfrac{(9\times 10^9)(15\times 10^{-9})}{0.04^2}\right]\hat i$$ $$E_{net}=(\color{red}{\bf 1.41\times 10^5}\;{\rm N/C})\;\hat i$$
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