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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.

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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?

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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.

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

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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.

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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 ^

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Questions & Answers

if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Jaffar
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
Who is ISSAAC NEWTON
LOAK Reply
he's the father of 3 newton law
Hawi
he is Chris Issaac's father :)
Ethem
Sir Isaac Newton's name comes in the list of great scientists in this world
himanshu
He is a far greatest, recognized scientist for his laws, 1,2,3 in motion, dynamic etc
Hlehle
Practice Key Terms 6

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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