Electric Field and Electric Field Lines

Instead of asking "what force acts here", physics asks "what does the space around a charge look like" — the electric field turns a charge's influence into a map you can read at every point.

Definition — Electric field: the force per unit positive test charge at a point, E = F/q₀ (as q₀ → 0). SI unit: N·C⁻¹ or equivalently V·m⁻¹. It is a vector.

Field of a point charge

E = k·Q / r², directed radially outward from a positive charge and radially inward toward a negative charge. The test charge must be small enough not to disturb the source charge's distribution — hence the limit q₀ → 0.

Field lines and their rules

Field lines are imaginary curves whose tangent at any point gives the field direction.

• Start on positive charges, end on negative charges (or at infinity).
• Never cross — a crossing would mean two field directions at one point.
• Are denser where the field is stronger (line density ∝ field magnitude).
• Are continuous curves with no sudden breaks in charge-free space.
• Are always perpendicular to the surface of a conductor.

Superposition of fields

The net field of several charges is the vector sum E = E₁ + E₂ + E₃ + …, each term computed as if alone.

Exam Tricks & Tips

• 🎯 Field points AWAY from + and TOWARD − — set the direction before plugging in numbers.
• 🎯 Field lines never intersect; if a diagram shows crossing lines, it is wrong.
• 🎯 Uniform field = equally spaced parallel lines (as between parallel plates).
• 🎯 E = F/q₀ uses a POSITIVE test charge; the field exists whether or not a test charge is present.
• 🎯 Line density encodes strength — bunched lines mean a strong field, spread-out lines a weak one.
• ❌ Common mistake: thinking field lines are the actual paths of charges; they only show the field's direction, not particle trajectories.

Expected exam pattern

A 1-mark definition or unit, a 2-mark point-charge field or superposition numerical, and frequent conceptual/assertion-reason questions on the properties of field lines (no crossing, start/end, density).

Quick recap

E = F/q₀ = kQ/r², a vector pointing away from + charges and toward − charges. Field lines start on +, end on −, never cross, and crowd where the field is strong. Net field = vector sum of individual fields.

Cover the answer, recall, then check. 10 cards on the electric field.

Q1. Define electric field.
A1. The force per unit positive test charge at a point: E = F/q₀ (as q₀ → 0). It is a vector.

Q2. What are the SI units of electric field?
A2. N·C⁻¹, equivalently V·m⁻¹.

Q3. Field of a point charge Q at distance r?
A3. E = kQ/r², directed radially outward for +Q and inward for −Q.

Q4. Why must the test charge be vanishingly small?
A4. So it does not disturb the source charge distribution being measured.

Q5. In which direction do field lines point near a positive charge?
A5. Radially outward, away from the positive charge.

Q6. Can two electric field lines cross?
A6. No — a crossing would give two field directions at one point, which is impossible.

Q7. What does the density of field lines represent?
A7. The magnitude of the field — denser lines mean a stronger field.

Q8. What do field lines look like in a uniform field?
A8. Equally spaced parallel straight lines (e.g. between two parallel plates).

Q9. How do field lines meet a conductor's surface?
A9. Perpendicular to the surface.

Q10. How is the net field of several charges found?
A10. By vector superposition: E = E₁ + E₂ + E₃ + …

How does one charge "know" another is nearby, across empty space? Michael Faraday's answer was the electric field — an invisible influence a charge spreads through space, felt by any other charge that enters it. The field is the bridge between charge and force.

Electric field — the core idea

The electric field at a point is the force experienced per unit positive test charge placed at that point.

E = F / q₀ (units: N/C or V/m)

The field is a vector, pointing in the direction of the force on a positive charge. It exists whether or not a test charge is actually there — it is a property of the source charge and the space around it.

Beginner: field of a point charge

A single point charge Q sets up a field at distance r:

E = k Q / r² = Q / (4πε₀r²)

It points away from a positive charge and toward a negative charge. Once you know E, the force on any charge q placed there is simply F = qE.

Intermediate: why "test charge" must be small

The test charge q₀ must be vanishingly small so it does not disturb the source distribution (a large test charge could push the source charges around and change the very field you are measuring). Formally, E = lim(q₀→0) F/q₀.

Advanced: superposition of fields

For many charges, the net field is the vector sum of individual fields:

E_net = E₁ + E₂ + E₃ + …

Resolve into components, add, recombine. For a positive and negative charge of equal magnitude (a dipole), the fields combine to give the characteristic dipole pattern.

Electric field lines

Field lines are a visual map of the field. Rules you must know:

• They start on positive charges and end on negative charges (or at infinity).
• The tangent at any point gives the field direction there.
• Density of lines (lines per unit area) is proportional to field strength — crowded lines mean strong field.
• Lines never cross (the field has one unique direction at each point).
• Lines are continuous curves with no breaks in a charge-free region.
• They exert a lateral pressure (like stretched elastic) — explaining attraction and repulsion.

The number of lines from a charge is proportional to its magnitude, so a 2Q charge sprouts twice as many lines as Q.

Worked example

Find the electric field 20 cm from a point charge of +5 μC in air.

E = k Q / r² = (9 × 10⁹)(5 × 10⁻⁶) / (0.20)²
E = 45000 / 0.04 = 1.125 × 10⁶ N/C, directed radially outward.

Real-world / exam application

Field lines explain why charge collects at the sharp tips of a lightning rod (lines crowd there — strong field), how a Van de Graaff generator works, and how ink and paint are sprayed uniformly using charged fields. In exams, E = F/q and the superposition of point-charge fields are perennial one- and two-mark questions.

Exam tricks & shortcuts

• Field is strong where lines are dense, weak where sparse, zero where no lines pass.
• Uniform field ⇒ equally spaced parallel lines (as between capacitor plates).
• Mnemonic "TIN": Tangent gives direction, Intensity ∝ line density, Never cross.

Key formulas

• Electric field: E⃗ = F⃗/q₀ (N/C or V/m).
• Field of a point charge: E = kQ/r² (radially outward for +Q).
• Superposition: E⃗ = ΣE⃗ᵢ.
• Force on a charge: F⃗ = qE⃗.
• Field lines: start on +, end on −; density ∝ field strength; never cross.

The electric field is the force per unit positive test charge; it is a vector pointing away from positive charges.

Worked Example

Problem: Calculate the magnitude of the electric field at a point 10 cm from a point charge of +5 μC. (k = 9 × 10⁹ N·m²/C².)

Solution:
Step 1 — Write the expression for the electric field due to a point charge:
E = k q / r².

Step 2 — Convert to SI units:
q = 5 × 10⁻⁶ C, r = 10 cm = 0.10 m.

Step 3 — Substitute:
E = (9 × 10⁹)(5 × 10⁻⁶) / (0.10)².

Step 4 — Evaluate:
Numerator = 9 × 10⁹ × 5 × 10⁻⁶ = 4.5 × 10⁴.
Denominator = 0.01.
E = 4.5 × 10⁴ / 0.01 = 4.5 × 10⁶ N/C.

Step 5 — Direction: the field points radially away from the positive charge.

Answer: The electric field is 4.5 × 10⁶ N/C, directed away from the charge.