Electric force between point charges
Section: Electric Fields | Syllabus: Cambridge A Level Physics (9702)
Coulomb's Law
Charles-Augustin de Coulomb established that the force F between two point charges (Q_1 and Q_2) varies with their separation r following an inverse square law.
F = (Q_1 Q_2/4π_0 r^2) Permittivity of Free Space (_0)_0 ≈ 8.85 × 10^-12 F m^-1.
The constant k = (1/4π_0) ≈ 8.99 × 10^9 N m^2 C^-2.
Forces in the Atom: Electric vs Gravity
Consider a hydrogen atom (electron and proton separated by 0.053 nm):
- Electric Force: F_E = (e^2/4π_0 r^2) ≈ 8.2 × 10^-8 N.
- Gravitational Force: F_G = (G m_p m_e/r^2) ≈ 3.6 × 10^-47 N.
The electric force is approximately 10^39 times stronger than the gravitational force. In subatomic interactions, gravity is completely negligible.
Spherical Conductors
A uniformly charged sphere can be treated as a point charge at its center. This approximation is valid for any point outside the sphere's surface.
Worked Examples
Worked Example: Charges on a BalanceQuestion: Two identical charged spheres repell each other. The balance reading changes by 0.014 g when their centers are 10 cm apart. Calculate the charge on each sphere.
Solution1. Force F = mg = (0.014 × 10^-3 kg) × 9.81 = 1.37 × 10^-4 N.
2. F = k (Q^2/r^2) Q^2 = (F r^2) / k.
3. Q^2 = (1.37 × 10^-4 × 0.1^2) / (8.99 × 10^9) = 1.52 × 10^-16.
4. Q = √1.52 × 10^-16 = 1.2 × 10^-8 C (or 12 nC).
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