Coulomb's Law

Dictionary

Coulomb's law is the relationship between the force between two charges, the magnitude of the charges, and the distance between them.

Fe = kQQ/R2

Q = charge, measured in Coulombs (1 Coulomb = 6.24 x 1018 elementary charges)

Elementary charge = charge on an electron or a proton (1.602 x 10-19C)

R = separation distance between the charges

Fe = electric force

 

The Fe is a vector quantity.

A common convention is that if the force is negative (one of the charges is negative) then the force is attractive. It follows that if the force is positive, then the force is repulsive. This can become a confusing convention since there may be 2 attractive forces in opposite directions on a single charge (by 2 other charges), so we won't use this convention.

We can make things simple if we solve for magnitudes and compare them qualitatively as follows:

Example 1: What is the force on charge B due to the other charges?

The force on B is a result of the sum of the force due to A (FBA) and the force due to C (FBC)

FBA is repulsive (to the right)

FBC is attractive (also to the right)

The overall force must be the sum of both forces to the right…now we can calculate the overall force on B.

F = kQAQB/R2 + kQBQC/R2

(to the right)

 

Example 2: What is the force on charge A due to the other charges?

The force on A is the result of the sum of the force due to B (FAB) and the force due to C (FAC)

FAB is repulsive (to the left)

FAC is attractive (to the right)

The overall force must be the sum of both forces, one to the right and one to the left…now we can calculate the overall force on B.

 

F = kQAQB/R2 - kQAQC/R2    

(to the left since FAB is a larger force)

 

For more examples and discussion check out this link: Estat at Glenbrook

Electric force vectors can be added in 2 dimensions as well. Simply add them using the cosine law method discussed in previous units or resolve each vector into components and treat each dimension separately (also from previous units).