Electric Potential and Capacitors — Formula Sheet

V = W/q₀

V_AB = (V_B - V_A) = W_AB / q₀

V = (1/4πε₀) × (q/r)

V = Σ (qᵢ / 4πε₀rᵢ)

V_dipole = p cosθ / (4πε₀r²)

U = q₁q₂ / (4πε₀r₁₂)

U = (1/4πε₀) × [q₁q₂/r₁₂ + q₁q₃/r₁₃ + q₂q₃/r₂₃]

U₀ = -pE cosθ = -p·E

C = Q/V

C_sphere = 4πε₀r = r / (9×10⁹)

C₀ = ε₀A/d

C = Kε₀A/d = KC₀

Potential difference between two points A and B

V_AB = V_B - V_A = W_AB / q₀, where W_AB is work done and q₀ is the test charge.

An electric dipole consists of two equal and opposite charges +q and -q separated by distance 2l, with dipole moment p = q × 2l directed from -q to +q.

Potential at a point P at distance r from centre, making angle θ with dipole axis: V = p cosθ / (4πε₀ r²).

Electric field at a point equals the negative rate of change of potential with distance: E = -ΔV/Δr.

For a uniform field

E = (V_A - V_B) / d, where d is the separation between points A and B.

SI unit of capacitance

farad (F). 1 F = 1 C/V. Common units: microfarad (μF = 10⁻⁶ F) and picofarad (pF = 10⁻¹² F).

Potential is maximum on positive end of dipole axis (θ = 0°)

Potential energy for two charges

U = kq₁q₂/r

For an electric dipole with dipole moment p = q × 2l, the potential at a point P at distance r and angle θ from the axis is: V = (p cosθ)/(4πε₀r²).