Electric Field & Potential

The two concepts that connect Coulomb's Law to everything else in electrostatics.

1. Electric Field (E⃗)

🧠 The Concept That Changes Everything

Instead of "charges exert forces," think "charges create fields, and fields exert forces." This shift in thinking is what separates JEE toppers from average students.

Definition

Electric field at a point is the force per unit positive charge at that point.

E⃗ = F⃗/q₀

Due to Point Charge

E = k Q/r²

Direction: Radially outward if Q > 0, inward if Q < 0

❌ Common Confusion

Electric field exists even if no test charge is present. It's a property of space created by source charges. Students often think field = force. NO. Field × charge = force.

Key Properties

Vector quantity (has magnitude and direction)
Follows superposition principle
Independent of test charge
Units: N/C or V/m (both equivalent)

2. Electric Potential (V)

🔬 Why Potential > Field for Calculations

Potential is scalar—no vector addition mess. In JEE numericals, always try finding potential first, then derive field if needed: E = -dV/dr.

Definition

Electric potential at a point is the work done per unit charge to bring a positive charge from infinity to that point.

V = W/q₀ = k Q/r

Relation with Field

E = -dV/dr (for radial field)

Negative sign: Field points from high to low potential

Potential Energy vs Potential

Potential Energy (U)

Energy of system of charges

U = k q₁q₂/r

Depends on both charges

Potential (V)

Property of location in field

V = k Q/r

Independent of test charge

🎯 Pro Strategy

Relationship: U = qV
If you know potential V at a point, energy of charge q there is simply U = qV. This one-liner solves 30% of JEE numericals instantly.

3. Equipotential Surfaces

Definition

Surfaces where electric potential is constant.

Properties (MCQ Favorites)

Property 1: No Work Done ▼

Moving a charge along equipotential surface requires zero work because ΔV = 0.

JEE Trap: "Work done moving charge from A to B on same equipotential?" Answer: Zero, regardless of path.

Property 2: Perpendicular to Field Lines ▼

Electric field is always perpendicular to equipotential surfaces.

Why? If E had component along surface, potential would change—contradiction.

Property 3: Spacing ∝ 1/E ▼

Closer equipotential surfaces → Stronger field

Farther apart → Weaker field

Visual Check: In diagrams, count surface density to judge field strength.

For Different Charge Distributions

Point charge: Concentric spheres
Infinite line charge: Coaxial cylinders
Infinite plane: Parallel planes
Dipole: Complex 3D surfaces (JEE Advanced)

4. Electric Dipole Deep Dive

🔬 JEE's Favorite Sub-Topic

Dipole appears in 80% of JEE electrostatics problems. Master this, and you're unstoppable.

What is a Dipole?

Two equal and opposite charges (+q and -q) separated by distance 2a.

Dipole Moment: p = q × 2a

Direction: From -q to +q

Critical Formulas (Memorize These)

Axial Line (End-on)

E = 2kp/r³

Direction: Along axis

Equatorial Line (Broadside)

E = kp/r³

Direction: Opposite to p⃗

Torque in Field

τ = pE sin θ

Maximum at θ = 90°

Potential Energy

U = -pE cos θ

Minimum at θ = 0°

🎯 Quick Check: Ratio Trick

E_axial / E_equatorial = 2 (at same distance)
Remember this ratio. It appears in at least 1 JEE question every year.

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