Coulomb’s Law

Electric Force and Electric Field

Coulomb's Law• Coulomb determined

– Force is attractive if charges are opposite sign

– Force is proportional to the product of the charges q1 and q2 and is along the lines joing them

– Force inversely proportional to the square of distance between the charges

i.e.– |F12| |Q1| |Q2| / r12

2

– or

– |F12|= k |Q1| |Q2| / r122

Coulomb's Law

• Units of constant can be determined from Coulomb's Law

• Colomb (and others since) have determined this constant which (in a vacuum) in SI units is– k = 8.987.5x109 Nm2C-2

• k is normally expressed as k = 1/40

– where is the permittivity of free space

Coulomb's Law

Vector form of Coulomb’s Law

+

+

Q1

Q2r12

12r̂

21F

12F

12F

+

21F

-

r12 is a vector connecting the two charges. is a unit vector in this direction

12r̂

Sample Problem

PBA+ - +

6 cm 4 cm

2 nC 5 nC 1 nC

NFAP6

2

999 108.1

1.0

101102109

NFBP5

22

999 108.2

)104(

101105109

Resultant F on P = FBP – FAP = 2.6210-5 N.

Direction: To the left (attraction)

Force from many charges

Superposition

Force from many charges

+

41F

31F

21F

Q1

-Q2

+Q4

- Q3

4131211 FFFF

Force on charge is vector sum of forces from all charges

Principle of superposition