Coulomb's Law and Electric Field Intensity

Why it matters

Understanding Coulomb's Law and Electric Field Intensity is crucial for analyzing and designing electrical systems, as they describe the forces between charged particles and the behavior of electric fields. These concepts are fundamental in fields like electronics, telecommunications, and power engineering.

Key ideas

• Coulomb's Law: Describes the force between two point charges. The force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
• Electric Field Intensity (E): A vector quantity that represents the force experienced by a unit positive charge placed in a field. It is defined as the force per unit charge.
• Superposition Principle: The net electric field due to multiple charges is the vector sum of the electric fields due to individual charges.

Formulas

• Coulomb's Law: F = k * (|q1 * q2| / r^2)
  • F: Force between the charges (N)
  • k: Coulomb's constant (8.9875 × 10^9 N·m²/C²)
  • q1, q2: Magnitudes of the charges (C)
  • r: Distance between the charges (m)
• Electric Field Intensity: E = F / q
  • E: Electric field intensity (N/C)
  • F: Force experienced by the charge (N)
  • q: Magnitude of the charge (C)

Worked example

Point charges q1 = +2 μC and q2 = −3 μC are 0.5 m apart in vacuum.

1. Force magnitude = 8.9875×10^9 × (2×10^−6)(3×10^−6)/(0.5)² = 0.2157 N. The charges attract.
2. The field due to q1 at the location of q2 (excluding q2’s self-field) is E1 = kq1/r² = 71,900 N/C, directed away from q1.
3. Force on q2 is q2 E1, opposite to E1 because q2 is negative; magnitude 3×10^−6 × 71,900 = 0.2157 N. For the vector relation E = F/q, q is signed. F/|q| gives a magnitude only. The stated Coulomb constant applies in vacuum; a uniform linear medium uses its permittivity.

Common mistakes

• Confusing the direction of the force or electric field, especially with negative charges.
• Forgetting to square the distance in Coulomb's Law.
• Not converting microcoulombs to coulombs correctly.

For GATE EE

Questions often involve calculating forces between charges, determining electric field intensity at a point, or using the superposition principle. Practice problems with varying charge configurations and distances.

Quick check

1. What is the unit of electric field intensity?
2. How does the force between two charges change if the distance between them is doubled?
3. What is the value of Coulomb's constant?

Answers: 1. N/C 2. It becomes one-fourth. 3. 8.9875 × 10^9 N·m²/C²