Section 4.2: Coulomb’s Law
Coulomb’s Law describes the electrostatic force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Coulomb’s Law Formula:
- \( F = k \frac{|q_1 q_2|}{r^2} \)
- Where \( k = 9 \times 10^9 \, \text{N·m²/C²} \)
- Direction: Along the line joining the two charges; repulsive for like charges, attractive for opposite charges.
Example 1
Two charges of 3 μC and 5 μC are placed 0.4 m apart. Find the electrostatic force between them.
\( F = k \frac{q_1 q_2}{r^2} = (9 \times 10^9)(3 \times 10^{-6})(5 \times 10^{-6}) / 0.4^2 = 0.84375 \, \text{N} \)
Example 2
Two charges, +2 μC and -4 μC, are 0.2 m apart. Determine the magnitude and direction of the force.
\( F = (9 \times 10^9)(2 \times 10^{-6})(4 \times 10^{-6}) / 0.2^2 = 1.8 \, \text{N} \) towards the negative charge.
Practice Problems
- Find the force between two charges, 6 μC and 3 μC, separated by 0.5 m.
- Two charges, -2 μC and +4 μC, are 0.3 m apart. Compute the electrostatic force.
- A 1 μC charge is placed 0.1 m from a 2 μC charge. Find the force and state the direction.
- Three charges at the vertices of a triangle: calculate net force on one charge.
- Two charges of equal magnitude 5 μC separated by 0.2 m. Find the force between them.
- A charge of 2 μC is placed at the midpoint between two -3 μC charges 0.4 m apart. Compute net force.
- Charges +3 μC and -5 μC are 0.6 m apart. Find the magnitude and direction of force.
- Two small spheres carry 4 μC and 1 μC separated by 0.1 m. Calculate the force.
- Two charges, 2 μC and 3 μC, are placed on a line with 0.25 m separation. Find the force.
- A particle with charge +1 μC is 0.5 m from a -2 μC particle. Find the electrostatic force.