Electrostatics

Why it matters

Electrostatics is fundamental in understanding how electric charges interact when they are at rest. This knowledge is crucial for designing and analyzing electrical and electronic systems, such as capacitors and insulators, which are integral components in circuits and devices.

Key ideas

• Electric Charge: A fundamental property of matter that causes it to experience a force when placed in an electric field. Charges can be positive or negative.
• Coulomb's Law: Describes the force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
• Electric Field (E-field): A vector field around a charged object where a force would be exerted on other charges. It is defined as the force per unit charge.
• Electric Potential: The external quasistatic work per unit positive charge relative to a reference, often infinity for localized charge distributions. It is a scalar quantity.
• Gauss's Law: Relates the electric flux through a closed surface to the charge enclosed by that surface.

Formulas

• Coulomb's Law: F = k * (q1 * q2) / r^2
  • F: Force between charges (N)
  • k: Coulomb's constant (8.9875 × 10^9 N·m²/C²)
  • q1, q2: Signed charges (C); the scalar radial coefficient is negative for unlike charges
  • r: Distance between the charges (m)
• Electric Field: E = F / q
  • E: Electric field (N/C)
  • F: Force (N)
  • q: Charge (C)
• Electric Potential: V = W / q
  • V: Electric potential (V)
  • W: Work done (J)
  • q: Charge (C)
• Gauss's Law: Φ = Q_enclosed / ε₀
  • Φ: Electric flux (N·m²/C)
  • Q_enclosed: Charge enclosed (C)
  • ε₀: Permittivity of free space (8.854 × 10^-12 C²/N·m²)

Worked example

Problem: Calculate the electric force between two charges of 3 μC and -2 μC separated by a distance of 0.5 m.

1. Identify the given values:
   • q1 = 3 × 10^-6 C
   • q2 = -2 × 10^-6 C
   • r = 0.5 m
   • k = 8.9875 × 10^9 N·m²/C²
2. Use Coulomb's Law: F = k * (q1 * q2) / r^2
3. Substitute the values: F = 8.9875 × 10^9 * (3 × 10^-6 * -2 × 10^-6) / (0.5)^2
4. Calculate: F = 8.9875 × 10^9 * (-6 × 10^-12) / 0.25
5. Simplify: F = -0.2157 N

Answer: -0.2157 N (The negative sign indicates an attractive force.)

Common mistakes

• Confusing the direction of the electric field and force.
• Forgetting to square the distance in Coulomb's Law.
• Misplacing the negative sign for attractive forces.
• Assuming Gauss’s law alone gives an easy field calculation without sufficient symmetry; the law itself is always valid.

For GATE EC

Questions often involve calculating forces between charges, electric fields, and potentials. Practice problems on applying Gauss's Law to different geometries and understanding the concept of electric flux.

Quick check

1. What is the unit of electric charge?
2. State Coulomb's Law in words.
3. What does a negative radial force coefficient mean for the signed point-charge formula?

Answers: 1. Coulomb (C) 2. The force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. 3. An attractive force.