<< Chapter < Page Chapter >> Page >

We can’t add these forces directly because they don’t point in the same direction: F 12 points only in the − x -direction, while F 13 points only in the + y -direction. The net force is obtained from applying the Pythagorean theorem to its x - and y -components:

F = F x 2 + F y 2

where

F x = F 23 = 1 4 π ε 0 q 2 q 3 r 23 2 = ( 8.99 × 10 9 N · m 2 C 2 ) ( 4.806 × 10 −19 C ) ( 8.01 × 10 −19 C ) ( 4.00 × 10 −7 m ) 2 = 2.16 × 10 −14 N

and

F y = F 21 = 1 4 π ε 0 q 2 q 1 r 21 2 = ( 8.99 × 10 9 N · m 2 C 2 ) ( 4.806 × 10 −19 C ) ( 3.204 × 10 −19 C ) ( 2.00 × 10 −7 m ) 2 = 3.46 × 10 −14 N .

We find that

F = F x 2 + F y 2 = 4.08 × 10 −14 N

at an angle of

ϕ = tan −1 ( F y F x ) = tan −1 ( 3.46 × 10 −14 N −2.16 × 10 −14 N ) = −58 ° ,

that is, 58 ° above the − x -axis, as shown in the diagram.

Significance

Notice that when we substituted the numerical values of the charges, we did not include the negative sign of either q 2 or q 3 . Recall that negative signs on vector quantities indicate a reversal of direction of the vector in question. But for electric forces, the direction of the force is determined by the types (signs) of both interacting charges; we determine the force directions by considering whether the signs of the two charges are the same or are opposite. If you also include negative signs from negative charges when you substitute numbers, you run the risk of mathematically reversing the direction of the force you are calculating. Thus, the safest thing to do is to calculate just the magnitude of the force, using the absolute values of the charges, and determine the directions physically.

It’s also worth noting that the only new concept in this example is how to calculate the electric forces; everything else (getting the net force from its components, breaking the forces into their components, finding the direction of the net force) is the same as force problems you have done earlier.

Check Your Understanding What would be different if q 1 were negative?

The net force would point 58 ° below the − x -axis.

Got questions? Get instant answers now!

Summary

  • Coulomb’s law gives the magnitude of the force between point charges. It is
    F 12 ( r ) = 1 4 π ε 0 q 1 q 2 r 12 2 r ^ 12

    where q 2 and q 2 are two point charges separated by a distance r . This Coulomb force is extremely basic, since most charges are due to point-like particles. It is responsible for all electrostatic effects and underlies most macroscopic forces.

Conceptual questions

Would defining the charge on an electron to be positive have any effect on Coulomb’s law?

Got questions? Get instant answers now!

An atomic nucleus contains positively charged protons and uncharged neutrons. Since nuclei do stay together, what must we conclude about the forces between these nuclear particles?

The force holding the nucleus together must be greater than the electrostatic repulsive force on the protons.

Got questions? Get instant answers now!

Is the force between two fixed charges influenced by the presence of other charges?

Got questions? Get instant answers now!

Problems

Two point particles with charges +3 μ C and +5 μ C are held in place by 3-N forces on each charge in appropriate directions. (a) Draw a free-body diagram for each particle. (b) Find the distance between the charges.

Got questions? Get instant answers now!

Two charges +3 μ C and +12 μ C are fixed 1 m apart, with the second one to the right. Find the magnitude and direction of the net force on a −2-nC charge when placed at the following locations: (a) halfway between the two (b) half a meter to the left of the +3 μ C charge (c) half a meter above the +12 μ C charge in a direction perpendicular to the line joining the two fixed charges

a. charge 1 is 3 μ C ; charge 2 is 12 μ C , F 31 = 2.16 × 10 −4 N to the left,
F 32 = 8.63 × 10 −4 N to the right,
F net = 6.47 × 10 −4 N to the right;
b. F 31 = 2.16 × 10 −4 N to the right,
F 32 = 9.59 × 10 −5 N to the right,
F net = 3.12 × 10 −4 N to the right,
Three charges are shown. Charge 1 is a 3 micro Coulomb charge at the bottom left. Charge 2 is a 12 micro Coulomb charge at the bottom right, 1 meter to the right of charge 1. Charge 3 is a minus 2 nano Coulomb charge 0.5 meters above charge 2. The charges define a right triangle, with charge 2 at the right angle. The angle at the vertex with charge one is theta. The forces on charge three are shown. F 3 1 points down and to the left, toward charge 1. Force F 3 2 points vertically down. ;
c. F 31 x = −2.76 × 10 −5 N i ^ ,
F 31 y = −1.38 × 10 −5 N j ^ ,
F 32 y = −8.63 × 10 −4 N j ^
F net = −2.76 × 10 −5 N i ^ 8.77 × 10 −4 N j ^

Got questions? Get instant answers now!

Questions & Answers

the diagram of the digestive system
Assiatu Reply
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 6

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

Ask