Coulomb's Law

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Discussion

introduction

The force between two point charges is …

• directly proportional to the magnitude of each charge (q₁, q₂),
• inversely proportional to square of the separation between their centers (r),
• directed along the line connecting their centers (r).

This relationship is known as Coulomb's Law. Charles Augustin de Coulomb (1736-1806) France. As an equation it is usually written in one of two forms …

F =	ke	q1q2		or	F =	1		q1q2
		r2				4πε0		r2
ke =	electrostatic constant 8.99 × 109 N·m2/C2				ε0 =	vacuum permittivity 8.85 × 10−12 C2/N·m2

text

• When two charges have the same sign
  their product is positive,
  which means the force vector is directed with the separation vector
  and the action is repulsive.
• When two charges have the opposite sign
  their product is negative,
  which means the force vector is directed against the separation vector
  and the action is attractive.

 

Summary

• The force between two point charges is …
  • directly proportional to the magnitude of each charge (q₁, q₂),
  • inversely proportional to square of the separation between their centers (r),
  • directed along the line connecting their centers (r).
• This relationship is known as Coulomb's Law.
• As an equation it is usually written in one of two forms …

F =	ke	q1q2		or	F =	1		q1q2
		r2				4πε0		r2
ke =	electrostatic constant 8.99 × 109 N·m2/C2				ε0 =	vacuum permittivity 8.85 × 10−12 C2/N·m2

Problems

practice

1. Compare the electrostatic and gravitational forces between …
   1. an electron and proton in a hydrogen atom (the radius of the electron's orbit is about 53 pm)
   2. two protons in a helium nucleus with two neutrons between them (the radius of a neutron is about 1.2 fm)
   Solution …
   1. Answer it.
   2. Answer it.
2. If the moon were held in its orbit by an electrostatic rather than gravitational force …
   1. What quantity of charge would be needed?
   2. How many elementary charges is this?
   If all of the charge came from the separation of hydrogen atoms into electrons and protons …
   3. What mass of hydrogen would be required?
   4. How many liters of H₂ gas at STP would be required?
   Solution …
   1. Answer it.
   2. Answer it.
   3. Answer it.
   4. Answer it.
3. Given three charges in a standard coordinate system, calculate the magnitude and direction of the net electrostatic force on each.
   1. +10 μC at (0 m, 0 m)
   2. −20 μC at (0 m, +3 m)
   3. +25 μC at (−4 m, 0 m)
   Solution …
   1. Answer it.
   2. Answer it.
   3. Answer it.
4. Write something completely different.
   • Answer it.

numerical

1. problems

Resources

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