ELECTROSTATICS

Electrostatic Potential & dipole

Use: Notes + Revision

Electrostatic Potential Energy

2 Charges

U = (1 / 4π ε₀) (Q₁Q₂ / r)

Like charges → U positive (repulsive energy)
Unlike charges → U negative (attractive energy)
System energy = sum of all pair energies
No. of pairs = n(n-1)/2

Work Done

Potential

W = q (Vᴮ − Vᴬ)

Moving charge from A to B
If VB < VA → work negative
Example: w = 1 × (-500 − 500) = -1000 J
Superposition: algebraic sum of potentials

Zero Potential

Special Points

Like charges → no zero potential point
Unlike charges → two zero potential points
Inside point depends on Q₁ + Q₂
Outside point depends on Q₁ − Q₂

Potential of Conducting Sphere

Sphere

Inside → V = constant
Surface → V = kQ / R
Outside → V = kQ / r
Charge flows high potential → low potential
Final potential equal after connection

Electric Field & Potential

Relation

E = − dV/dr

Eₓ = − ∂V/∂x
Eᵧ = − ∂V/∂y
E_z = − ∂V/∂z
ΔV = − ∫ E·dr

Equipotential Surface

Rules

Field lines ⟂ equipotential surface
Work done on surface = 0
No two equipotential surfaces intersect
Uniform field → parallel planes

Dipole

Moment

p = q (2l)

Direction: −Q to +Q
V = k p cosθ / r²
E_equatorial = k p / r³
E_axial = 2k p / r³

Torque & Potential Energy

Dipole in Field

τ = pE sinθ

Max torque at θ = 90°
Min torque at θ = 0°
U = − pE cosθ
Stable: θ = 0° (U minimum)
Unstable: θ = 180° (U maximum)

Force in Non-Uniform Field

Advanced

Fₓ = p (dE/dx) cosθ
Both translatory & rotational motion possible
dE = small change in field at two charge positions

Minimum distance: d_min = 2kqQ / mv²