1. PHY 102: Lecture 1B
1.4 Charging Objects
1.5 Force between Charges

2. PHY 102: Lecture 1B Electric Charge
1.4
Charging Objects

3. Charging by Contact - 1
When a negatively charged rubber rod is rubbed on a metal object some of the excess electrons from the rod are transferred to the metal object
When the rod is removed the sphere is left with a negative charge distributed over its surface
When a positively charged rod is rubbed on a metal object some of the electrons from the metal object are transferred to the rod
When the rod is removed the sphere is left with a positive charge distributed over its surface
The process of giving one object a net electric charge by placing it in contact with another object that is already charged is known as charging by contact

4. Charging by Contact - 2

5. Charging by Induction - 1
A negatively charged rod is brought close to, but does not touch, a metal sphere
In the sphere, the free electrons closest to the rod, move to the other side
The part of the sphere nearest the rod becomes positively charged and the part farthest away becomes negatively charged
These positively and negatively charged regions have been “induced” to form because of the repulsive force between the negative rod and the free electrons in the sphere
If the rod were removed, the free electrons would return to their original places, and the charge regions would disappear

6. Charging by Induction - 2
The earth is a good electrical conductor
When a metal wire is attached between the sphere and the ground some of the free electrons leave the sphere and distribute themselves over the much larger earth
If the ground wire is then removed, followed by the rubber rod, the sphere is left with a positive net charge
The process of giving one object a net electric charge without touching the object to a second charged object is called charging by induction

7. Charging by Induction - 3

8. Charging by Induction - 4
If the sphere were made from an insulating material like plastic, instead of metal, the method of producing a net charge by induction would not work
Very little charge would flow through the insulating material and down the ground wire
The electric force would cause the positive and negative charges in the molecules of the insulating material to separate slightly, with the negative charge being “pushed” away from the negative rod
Although no net charge is created, the surface of the plastic does acquire a slight induced positive charge and is attracted to the negative rod

9. Charging by Induction - 5

10. PHY 102: Lecture 1 Electric Charge
1.5
Force between Charges

11. Forces on Electric Charges
Two electrically charged objects exert a force on one another
This is the Electric Force
Like charges repel and unlike charges attract each other

12. Charging by Rubbing - 1 Balloon is electrically neutral
Ten + and – charges
Sweater is also electrically neutral

13. Charging by Rubbing - 2 Rub balloon on sweater
Electrons (-) transfer from sweater to balloon
Balloon is negatively charged
Sweater is positively charges

14. Charging by Rubbing - 3 Separate the balloon and sweater
It is clear that the balloon is negatively charged
It is clear that the sweater is positively charged
Let the balloon go

15. Charging by Rubbing - 4
The negatively charged balloon is attracted to the positively charged sweater
Opposite charges attract

16. Charging by Induction - 1
Neutral balloon is brought close to wall
Nothing happens

17. Charging by Induction - 2
Negatively charged balloon is brought close to the wall
The negative charge on the balloon repels the negative charge on the wall
The wall is still neutral but the negative and positive charges separate slightly
The negative balloon is attracted to the closer positive charge on the wall

18. PHY 102: Lecture 1B Electric Charge
1.5 Force between Charges

19. Charles Coulomb (1736 – 1806) 1784 French Engineer
Did static electricity experiments
Built from the work of Benjamin Franklin
Measured strength of electric force

20. Coulomb’s Law
The magnitude F of the electrostatic force exerted by one point charge q1 on another point charge q2 is
r is the distance between charges
k = 8.99 x 109 Nm2/C2 in SI units
Sometimes k = 1/(40)
0 is called the permittivity of free space
0 = 1/(4k) = x C2/(Nm2)
Electrostatic force is directed along the line joining the charges
It is attractive if the charges have unlike signs
It is repulsive if the charges have like signs

21. Coulomb’s Law
Force on a Point Charge Due to Two or More Other Point Charges
We have discussed the electrostatic force on a point charge (magnitude |q1|) due to another point charge (magnitude |q2|)
Suppose that a third point charge (magnitude |q3|) is present
What is the net force on q1 due to both q2 and q3?
First, find the magnitude and direction of the force exerted on q1 by q2 (ignoring q3)
Then, determine the force exerted on q1 by q3 (ignoring q2)
The net force on q1 is the vector sum of these forces

22. Problem 2 Two spheres are separated by distance of 1.80 x 10-3 m
The spheres are initially electrically neutral and are very small compared to the distance between them
Each sphere gets same negative charge due to addition of electrons
Each sphere experiences an electrostatic force that has a magnitude of 4.55 x N
How many electrons did it take to the produce charge on one sphere?
F =kqq/r2
4.55 x = 8.99 x 109 x q2 / (1.80 x 10-3)2
4.55 x x (1.80 x 10-3)2 / 8.99 x 109 = q2
1.64 x = q2
q = 1.28 x 10-18
q = Ne
N = number of electrons = 1.28 x / 1.60 x 10-19
N = 8

23. Problem 3
Two objects, whose charges are +1.0 C and -1.0 C, are separated by 1.0 km
Find the magnitude of the attractive forces that either charge exerts on the other
Equivalent to weight of 900 kg mass
Equivalent to weight of 2000 pounds

24. Problem 4
In the Bohr model of the hydrogen atom, the electron (charge=-e) is in a circular orbit about the nuclear proton (charge=+e) at a radius of 5.29 x m ( nm)
The mass of the electron is 9.11 x kg
Determine the speed of the electron
Centripetal force = Coulomb’s Force

25. Problem 5 - 1 Three point charges lie along the x axis
Determine the magnitude and direction of the net electrostatic force on q1

26. Problem 5 - 2
Magnitude of the forces
Direction of net force