Can you explain how they get to this solution? ### Page 12 of 274## Problem 63: Electrostatic Force on a Charge in a Square Configuration**Problem Statement:**63. What is the force on the charge \( q \) at the lower-right-hand corner of the square shown here?**Diagram:**The diagram shows a square with sides of length \( a \). There are four charges, each denoted as \( q \), positioned at the corners of the square. Specifically:- The charges are located at the upper-right, upper-left, lower-right, and lower-left corners of the square.- The sides of the square are labeled as \( a \), and the distance between each charge along the sides is \( a \).\[\begin{array}{c|c|c}& & q \\a & & a \\& & q \\\hlineq & & q \\\end{array}\]**Solution:**The diagonal is \(\sqrt{2}a\) and the components of the force due to the diagonal charge have a factor \(\cos \theta = \frac{1}{\sqrt{2}}\).### Detailed Explanation:1. **Identifying Forces:** - To find the force on the charge at the lower-right hand corner, consider the contributions from the other three charges. - Each charge \( q \) exerts a Coulomb force on the charge at the lower-right hand corner.2. **Calculating Forces:** - **Side Charges:** - The force due to the charge directly to the left (at distance \( a \)). - The force due to the charge directly above (at distance \( a \)). - **Diagonal Charge:** - The force due to the charge at the diagonally opposite corner (at distance \( \sqrt{2}a \)).3. **Components of the Force:** - For the diagonal charge, resolve the force into its \( x \)-component and \( y \)-component. - The angle between the side and the diagonal is \( 45^\circ \), leading to components along both axes with a factor of \(\cos 45^\circ = \frac{1}{\sqrt{2}}\).4. **Vector Addition:** - Sum the forces vectorially considering the contributions from each charge.**Summary:**By calculating the forces from each of the contributing charges and OpenStax **University Physics Volume II****Unit 2: Electricity and Magnetism****Chapter 5: Electric Charges and Fields**\[ \mathbf{F}_{\text{net}} = \left[ k \frac{q^2}{a^2} + k \frac{q^2}{2a^2} \frac{1}{\sqrt{2}} \right] \hat{i} - \left[ k \frac{q^2}{a^2} + k \frac{q^2}{2a^2} \frac{1}{\sqrt{2}} \right] \hat{j} \]**64. Point charges** \( q_1 = 10 \, \mu C \) **and** \( q_2 = -30 \, \mu C \) **are fixed at** ...

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Answered: 63. What is the force on the charge q…

Science

Physics

63. What is the force on the charge q at the lower-right-hand corner of the square shown here? q a q a a 9

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter22: Electric Fields

Section: Chapter Questions

Problem 12P

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