Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 16, Problem 14P
To determine

To find: The magnitude and direction of the force on each charge.

Expert Solution & Answer
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Answer to Problem 14P

The magnitude of force on each charge is same that is 6.2×107N but the direction of force is different. Force on B will make 45 with the positive x axis, force on C will make 45 and force on D will make 225 .

Explanation of Solution

Given:

A charge of 6.00mC is placed at each corner of a square 0.100m on a side.

Formula used:

Consider the figure shown below.

  Physics: Principles with Applications, Chapter 16, Problem 14P

The magnitudes of the individual forces can be found using Coulomb's law. The direction of each force will be along the line connecting qA to qB,qc and qD . The forces at the upper left corner of the square are the vector sum of the forces due to the other three charges.

  FA=FB+Fc+FD

Calculation:

Let the variable r represents the 0.10m length of a side of the square, and let the variable q represents the 6.0mC charge at each corner.

The force on the charge at A due to the other 3 charges is,

  FA=FB+Fc+FD

  =kq[qB(i^)rAB2+qCrAC2(sin45(j^)+cos45(i^))+qD(j^)rAD2]

  =kq2[(1r2+12r2cos45)(i^)+(12r2sin45+1r2)(j^)]

  =kq2r2[(1+122)(i^)+(122+1)(j^)]

Hence,

  |FA|=kq2r2[(1+122)2+(122+1)2]1/2=2kq2r2(1+122)=kq2r2(2+12)=(9×109Nm2/C2)(6×103C)2(0.1m)2(2+12)=6.2×107N

The direction is given as,

  θ=tan1(122+11+122)=135

Here, θ is the angle made with the positive x axis.

Hence, for each charge, the magnitude of net force is same that is 6.2×107N but the direction of force is different.

Force on B will make 45 with the positive x axis, force on C will make 45 and force on D will make 225

Chapter 16 Solutions

Physics: Principles with Applications

Ch. 16 - Prob. 11QCh. 16 - Prob. 12QCh. 16 - Prob. 13QCh. 16 - Prob. 14QCh. 16 - Prob. 15QCh. 16 - Prob. 16QCh. 16 - Prob. 17QCh. 16 - Assume that the two opposite charges in Fig....Ch. 16 - Consider the electric field at the three points...Ch. 16 - Why can electric field lines never cross?Ch. 16 - Show, using the three rules for field lines given...Ch. 16 - Given two point charges, Q and 2Q, a distance l...Ch. 16 - Consider a small positive test charge located on...Ch. 16 - A point charge is surrounded by a spherical...Ch. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5PCh. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - Prob. 10PCh. 16 - Prob. 11PCh. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - Prob. 15PCh. 16 - Prob. 16PCh. 16 - Prob. 17PCh. 16 - Prob. 18PCh. 16 - Prob. 19PCh. 16 - Prob. 20PCh. 16 - Prob. 21PCh. 16 - Prob. 22PCh. 16 - Prob. 23PCh. 16 - Prob. 24PCh. 16 - Prob. 25PCh. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - Prob. 29PCh. 16 - Prob. 30PCh. 16 - Prob. 31PCh. 16 - Prob. 32PCh. 16 - Prob. 33PCh. 16 - Prob. 34PCh. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - Prob. 38PCh. 16 - Prob. 39PCh. 16 - Prob. 40PCh. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Prob. 43PCh. 16 - Prob. 44PCh. 16 - Prob. 45PCh. 16 - Prob. 46PCh. 16 - Prob. 47PCh. 16 - Prob. 48PCh. 16 - Prob. 49PCh. 16 - Prob. 50PCh. 16 - Prob. 51PCh. 16 - Prob. 52GPCh. 16 - Prob. 53GPCh. 16 - Prob. 54GPCh. 16 - Prob. 55GPCh. 16 - Prob. 56GPCh. 16 - Prob. 57GPCh. 16 - Prob. 58GPCh. 16 - Prob. 59GPCh. 16 - Prob. 60GPCh. 16 - Prob. 61GPCh. 16 - Prob. 62GPCh. 16 - Prob. 63GPCh. 16 - Prob. 64GPCh. 16 - Prob. 65GPCh. 16 - Prob. 66GPCh. 16 - Prob. 67GPCh. 16 - Prob. 68GPCh. 16 - Prob. 69GPCh. 16 - Prob. 70GPCh. 16 - Prob. 71GPCh. 16 - Prob. 72GPCh. 16 - Prob. 73GP
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