Answered: Find the force acting between two…

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

Find the force acting between two charges q1=-10^-11C and q2=-10^-13C in a vaccum.The distance between the charges is 1cm.Make a drawing to show the direction of tge force acting on each other

Expert Solution

Step 1

Given:

The magnitude of the charge $q_{1}$ is $- 10^{- 11} C$ .

The magnitude of the charge $q_{2}$ is $- 10^{- 13} C$ .

The distance between the two charges is $1 cm$ .

Introduction:

The force of attraction between two alike charges or the force of repulsion between two like charges is directly proportional to the product of the magnitude of the two charges and inversely proportional to square of the distance between the two charges.

Step 2

Calculations:

Write the expression for the force of repulsion between two given charges.

$F = \frac{q_{1} q_{2}}{4 π ε_{0} r^{2}}$

Here, $q_{1}$ and $q_{2}$ are two charges, $ε_{0}$ is the permitivity of vacuum and $r$ is the distance of separation between them.

Substitute $- 10^{- 11} C$ for $q_{1}$ , $- 10^{- 13} C$ for $q_{2}$ , $8.85 \times 10^{- 12} \frac{C^{2}}{N . m^{2}}$ for $ε_{0}$ and $1 cm$ for $r$ in the above expression.

$\begin{array}{rcl} F & = & \frac{(- 10^{- 11} C) (- 10^{- 13} C)}{4 π (8.85 \times 10^{- 12} \frac{C^{2}}{N . m^{2}}) {(1 cm \frac{1 m}{100 cm})}^{2}} \\ = & 8.99 \times 10^{- 11} N \end{array}$

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