Coulomb’s LawForces and Fields Lesson 4

Charles Coulomb1736 -1806Discovered the inverse square law which

states that as you move charges apart the force between them decreases exponentially

Also showed that the force between two charged objects is proportional to the product of the charges

Unit of electrical charge is named after him

2

1eF r

1 2eF q q

The Torsion BalanceCoulomb used a

torsion balance (Physics 20 – universal gravitational constant) to determine “k” a universal value called Coulomb’s Constant.

http://www.youtube.com/watch?v=_5VpIje-R54

By measuring the amount of twist when the charges repelled each other, the force could be measured and the constant could be determined.

Coulomb’s Law describes the electrostatic forces between two charged objects.

Fe is the electrostatic forcek is Coulomb’s Constant q is the charge in Coulombs (C) ( the unit for charge is 1 C which equals the

charge of r is the distance separating the two charges (m)

1 22e

kq qF

r

29

2(8.99 10 )

N m

C

186.25 10 )electrons

Where:

Notice the similarities to Newton’s Law of Universal Gravitation

This shows only attraction while Coulomb’s Law can be used for both attractive and repulsive situations

Gravity is a weak force requiring large masses

Electric forces are very large in comparison and are effective with small charges

1 22g

Gm mF

r

Using Coulomb’s Law (1 D)To calculate the electric force between two

charges, always solve for the absolute value and ignore the sign on the charge. Determine whether the charges attract or repel at the end. ( A point charge is a small + or – charge.)

Eg) Calculate the magnitude of the electric force between two point charges of +4.00 uC and +3.00 uC when they are 4.50 cm apart.

1

2

0.045

4.00

3.00

r m

q C

q C

1 22

29 6 6

2

2

(8.99 10 )(4.00 10 )(3.00 10 )

(0.045 )

53.27

53.3 .

e

e

kq qF

r

N mC C

CFm

N

The magnitude of the repulsive force is N

Eg 2) A comb with 2.0 uC of charge is 1.5 m to the left from a hair with -3.0 uC of charge. Determine the force the hair exerts on the comb.

1

2

1.5

2.0

3.0

r m

q C

q C

1 2

2

29 6 6

2

2

2

2

(8.99 10 )(2.0 10 )(3.0 10 )

(1.5 )

2.4 10

2.4 10 .

e

e

kq qF

r

N mC C

CFm

N

The hair is pulling the comb with a force

of N right

Two point charges of and produce a force of

on each other. How far apart are these two

charges?

61.8 10 C 62.4 10 C32.2 10 N

1 22

1 2

29 6 6

2

3

(8.99 10 )(1.8 10 )(2.4 10 )

2.2 104.2

e

e

kq qF

r

kq qr

F

N mC C

CrN

m

Charges are usually in the range of microCoulombs. Only lightning strikes have a charge of 1 or 2 coulombs.

The electron’s charge is so important it is called an elementary charge. Its symbol is “e” and is also on your formula sheet.

NOTE:

Net electrical forceDetermine the net force on object B.

always interpret this to mean that theobject in question is free to move and theother objects are stationary.

Forces on B

Free body diagram

F C on B

1 22

9 2 2

2

10

8.99 10 / 1.00 2.00

(1.00 )

1.798 10 [ ]

e

e

e

kq qF

r

N m C C CF

m

F N left

F A on B

1 22

9 2 2

2

10

8.99 10 / 3.00 2.00

(2.00 )

1.3485 10 [ ]

e

e

e

kq qF

r

N m C C CF

m

F N right

Fnet

10 10

9

1.798 10 1.3485 10

4.50 10 [ ]

net ConB AonB

net

e

F F F

F N N

F N left

Example: Find the net electrical force on B.

A

B C

3.20 m

4.1 m

2.0 x 10 -6 C

-3.8 C

-1.5 C

1 22e

k q qF

r

29 6 6

2

2

8.99 10 2 10 3.8 10

3.2e

NmC C

CF

m

36.67 10eF N

AB

*down on B

BC 1 22e

kq qF

r

29 6 6

2

2

8.99 10 3.8 10 1.5 10

4.1e

NmC C

CF

m

33.05 10eF N

*

left on B

Draw Vector Diagram 3.05 x 10 -3 N

6.67 x 10 -3 N

ResultantF

2323R 1067.61005.3F

N103.7F 3R

N1005.3

N1067.6AO

tan 3

3

65

S65W,N103.7F 3R

*

Example: Calculate the gravitational force between an electron and a proton placed 1.0 cm apart.

221

g R

mmGF

22

27312

211

g m100.1

kg1067.1kg1011.9kg

Nm100.1

F

N100.1F 63g

*

Example: Calculate the electrical force between an electron and a proton placed 1.0 cm apart.

1 22e

kq qF

r

22

19192

29

electricalm100.1

C106.1C106.1C

Nm1099.8

F

N103.2F 24electrical

*

forcenalgravitatioforceelectrical:ratio

N100.1

N103.263

24

times10 39

Three point charges, A, B, and C, are arranged in a line as shown.

a. Determine the net electrostatic force acting on charge B.

b. The charge on object C is negative. Identify the sign of the charge (+ or -) on objecti. A.ii. B.

2 D Example:Three point charged objects are arranged in

a right angle as shown in the diagram.a. The charge on object A is positive. Identify

the sign of the charge (+ or -) on objecti. B. (negative)ii. C. (negative)

b. Determine the net electrostatic force acting on charge B.

Read WB p. 85-86 TB p. 532-6 Examples 10.3 to 10.6Do WB p.87 2-5,8,10,14,16,18,19