kinematics  
 
  Eddy currents  
 
  Lenz's law  
 
  Lines of fields  
 
  Insulators  
 
  Diff. Eqs   
 
  Constants  
 
  Units   
 
  home  
 
  ask us  
 

 








© The scientific sentence. 2010

Electrostatics: Coulomb's law



1. Coulomb's law



The electric force on the two stationary charges, qa and qb, distant by r, is given by the Coulomb's law:
The constant εo is called the permittivity of free space or vaccum.

The forces in the figure are oriented according to Newton's third law. Here the charges are of like sign.



2. Example: Three points charges



We want to calculate the Coulomb forces at the point c of charge - qc.

The charge on the point a is positive and the charge on the point c is negative, so the related forces are attractive.

Fac = Fca = k qa qc/n2.

Fac has no components on the y-axis.

The charge on the point b is negative and the charge on the point c is negative, so the related forces are repulsive.

Fbc = Fcb = k qb qc/(n2 + m2)

Fbc has two components: one on the y-axis, and the other on the z-axis.

The components of Fbc:

Fbc-y = Fbc cos(π - θ) = - Fbc cos θ
Fbc-z = + Fbc sin θ

Finally, the components of the net force F on c are:

Fy = - Fbc cos θ
Fz = - Fac + Fbc sin θ

cos θ = m/[m2 + n2]1/2
sin θ = n/[m2 + n2]1/2

F = [Fy 2 + Fz2]1/2
tg (β) = Fz/Fy




qa = + 1 µC
qb = - 2 µC
qc = - 3 µC

m = 4.0 m
n = 3.0 m

k = 9 x 109 N.m2 /C2

Therefore

Fbc = k qb qc/(n2 + m2)
= 9 x 109 (2 x 10-6) (3 x 10-6) /25 = 2.16 x 10-3 N

Fac = k qa qc/n2
= 9 x 109 (1 x 10-6) (3 x 10-6) /9 = 3.0 x 10-3 N

cos θ = 3/5
sin θ = 4/5

Fy = - 2.16 x 10-3 (3/5) = - 1.30 x 10-3 N
Fz = - Fac + Fbc sin θ =
- 3.0 x 10-3N + 2.16 x 10-3 (4/5) N =
- 3.0 x 10-3N + 1.72 N = - 1.18 x 10-3 N

F = [Fy 2 + Fz2]1/2 = [1.69 + 1.4]1/2 x 10-3
= 1. 75 x 10-3 N

tg (β) = Fz/Fy = - 1.18 /(- 1.30) = + 0.91
β = 42o.






 


chimie labs
|
Physics and Measurements
|
Probability & Statistics
|
Combinatorics - Probability
|
Chimie
|
Optics
|
contact
|


© Scientificsentence 2010. All rights reserved.