Electrostatics

NUST NET (Engineering) · Physics · Electricity. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Electrostatics is about charges at rest. Like charges repel and unlike charges attract with a force that follows an inverse square law, so doubling the distance cuts the force to a quarter.

The electric field at a point is the force on each coulomb of positive charge placed there. It is a vector, so the fields of several charges are added with direction. Electric potential is the work done per coulomb in bringing positive charge from infinity. It is a scalar, so potentials are added with their signs only.

A capacitor stores charge and energy. Capacitors combine the opposite way to resistors: they add directly in parallel and by reciprocals in series, where each one carries the same charge.

Rules to remember

Common mistake

Combining capacitors with the resistor rules. Capacitors add directly in parallel, and in series the total is smaller than the smallest capacitor.

Worked example

Capacitors of 3 μF and 6 μF are connected in series across a 12 V battery. What is the charge on each capacitor?

  1. Series capacitance: C = (3 × 6)/(3 + 6) = 18/9 = 2 μF.
  2. Charge drawn from the battery: Q = CV = 2 μF × 12 V = 24 μC.
  3. Capacitors in series carry the same charge, so each one holds 24 μC (check: 24/3 + 24/6 = 8 V + 4 V = 12 V).

Answer: 24 μC on each capacitor.

Practice questions

Try each one, then open the answer.

1. Taking k = 9 × 109 N m2 C−2, the electric potential at a distance of 0.30 m from a point charge of +2.0 nC is

  1. A
    200 V
  2. B
    18 V
  3. C
    60 V
  4. D
    5.4 V
Show answer

Answer: C. V = kq/r = 9 × 109 × 2.0 × 10−9/0.30 = 18/0.30 = 60 V. 200 V divides by r2, which gives the field strength in N C−1, not the potential.

2. Two identical small conducting spheres carry charges of +6 μC and −2 μC and attract each other with a force F. They are touched together and then returned to their original positions. The force between them is now

  1. A
    F/3, still attractive
  2. B
    4F/3, now repulsive
  3. C
    zero
  4. D
    F/3, now repulsive
Show answer

Answer: D. On touching, the total charge +4 μC is shared equally: +2 μC each. F ∝ q1q2, so the force changes from 6 × 2 = 12 units to 2 × 2 = 4 units, that is F/3, and like charges repel. 4F/3 comes from sharing 6 + 2 = 8 μC, ignoring the minus sign.

3. A parallel-plate capacitor is charged and then disconnected from the battery. A dielectric slab of relative permittivity 4 is then slid in to fill the gap. The energy stored

  1. A
    becomes 4 times as large
  2. B
    is unchanged
  3. C
    becomes one-quarter as large
  4. D
    becomes one-half as large
Show answer

Answer: C. Once disconnected, the charge Q is fixed. C becomes 4C, so U = Q2/2C falls to one-quarter. It would rise 4 times only if the battery stayed connected and kept V fixed.

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