Electric Field and Electric Potential

An electric field is the invisible region of force around a charge, just as a magnet has a magnetic field. Another charge placed in the field feels a force, and field strength is the force on a unit positive charge. Charge size and distance set both the direction and magnitude of that force. Slide charge and distance here to see how the field changes.

What is an Electric Field?

⚡ Region of Invisible Force

①Just as magnets have magnetic fields, charges have electric fields

②Another charge placed in a field experiences force

③Field strength E = force on a unit positive charge (+1 C)

④Analogy: an electric field is an "invisible wind" pushing charges

Field Lines and Equipotential Surfaces

Charge Q3 C

💡 Rules of Field Lines

①They leave (+) charges and enter (−) charges

②Denser lines = stronger field (density ∝ strength)

③Field lines never cross

④Equipotential surfaces are always perpendicular to field lines

⑤Distance 2× → density 1/4 → E also 1/4 (inverse-square law)

Coulomb's Law and Field Formula

Distance Between Charges5

Coulomb's Law

F = kQ₁Q₂r²

k = 9×10⁹ N·m²/C²; same signs → repel, opposite → attract

Electric Field Strength

E = kQr² [N/C = V/m]

Field at distance r from a point charge Q

📐 Key Relations

①F = qE — force on a charge = charge × field

②Distance 2× → force 1/4 (inverse-square law)

③Superposition: total field = vector sum from each charge

④Same direction → larger sum, opposite → smaller

Relation Between Field and Potential

Electric Potential

V = kQr [V]

Work to bring a +1 C from infinity to r

Field and Potential Difference

E = -ΔVΔr

Field = rate of change of potential — like the slope of a hill

🏔️ Topographic Analogy

①Potential = height: positive charges "roll" from high to low (+ → −)

②Field = slope: steep slope (large ΔV) → large force = strong field

③Equipotential = contour: moving along it → no work (force ⊥ motion)

④Around (+): closer means higher V; around (−): closer means lower V

Worked Examples

Example 1

A +0.5 C charge is placed where the electric field strength is 200 N/C. What electric force does it experience?

Use the force on a charge F = qE.

F = qE

Substitute q = 0.5 C, E = 200 N/C.

F = 0.5 × 200 = 100 N

▸ 100 N

F = qE is the force on a charge in a field. A positive charge feels a force in the same direction as the field.

Example 2

A voltage of 100 V is applied across parallel plates 0.02 m apart. What is the uniform field strength between them?

For parallel plates, the uniform field is E = V/d.

E = Vd

Substitute V = 100 V, d = 0.02 m.

E = 1000.02 = 5000 V/m

▸ 5000 V/m (= 5000 N/C)

Between parallel plates the field is uniform, E = V/d. The units V/m and N/C are equivalent.

Summary

Electric Field

E = kQr²

N/C

Potential

V = kQr

V (Volt)

CSAT-style

If the distance from a point charge doubles, how does the field strength at that point change?

①Doubles

②Halves

③Quadruples

④Becomes one quarter

⑤Stays the same

▸ ④ Becomes one quarter

A point charge field is E = kQ/r², inversely proportional to distance squared.

E = kQr²

If r doubles, r² quadruples → E becomes one quarter.

r→2r ⇒ E ∝ 1(2r)² = 14E

🎯 Exam Points

①Coulomb's law: F = kQ₁Q₂/r² (same → repel, opposite → attract)

②Field: E = kQ/r² — inverse square of distance (vector!)

③Potential: V = kQ/r — inverse of distance (scalar!)

④Moving on equipotential → work = 0 (force ⊥ motion)

⑤Field direction = direction of decreasing potential (high → low)

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Total Internal Reflection

Current and Resistance

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