Electric Field Explained: The Invisible Force Surrounding Every Charge
In one line: Electric Field — exam-ready notes in one glance.
- What a Field Really Is
- Field Lines: Drawing the Invisible
- Superposition: Fields Add as Arrows
- Uniform Fields
- Solved Examples
- This Physics in Your Daily Life
- Practice set (answers hidden — try first)
- Frequently Asked Questions
- Key Takeaways
- Exam Checklist
- FAQ
- How much of this page is exam-relevant?
- When should I revisit?
- The Thirty-Second Recap
- Explain It Simply
- Abbreviations That Recur Here
- The Plain-Word Walk
- The Numbers on One Table
- The Echo Round
JEE/NEET Physics · Electrostatics series · Part 2 of 8 · All parts →
- The field is the push a +1 C test charge would feel at a point — it exists even in empty space
- E = F/q (definition) · E = kQ/r² (point charge)
- In addition, field lines: out of +, into −; never cross; denser = stronger
- Multiple charges: fields add as vectors (superposition)
- Uniform field: parallel equally-spaced lines (between plates)
- Therefore, units: N/C = V/m — you will meet both in exams
A charge changes the space around it. Bring another charge near — even without touching — and it’s pushed or pulled. The ‘changed space’ is the electric field: invisible, everywhere around every charge, and the single most useful idea in Class 12 physics. Part 2 of the Electrostatics series.
- What a field really is
- What each letter means
- In addition, field lines: drawing the invisible
- Superposition: fields add as arrows
- Uniform fields
- Therefore, solved examples
- Common mistakes
- This physics in your daily life
- In addition, practice set
- Frequently asked questions
- Recap
What a Field Really Is
Don’t ask ‘how hard does charge A push charge B’ — ask ‘what push would a test charge feel at this point?‘ That push-per-coulomb, at every point in space, is the field:
+
−
lines: + → −, never cross, dense = strong
midpoint: both fields point + → − → they ADD (double)
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| E | electric field — push per unit positive charge at a point | N/C (same as V/m) |
| F | force a test charge q feels there | N |
| Q | the source charge creating the field | C |
| r | distance from the source’s CENTRE | m |
Same move as gravity’s g (Gravitation Part 9): g is ‘pull per kg’, E is ‘push per coulomb’. The field picture’s power: it lets space itself carry the physics — a charge doesn’t reach out; it changes its neighbourhood.
Here’s the definition logic in slow motion. Place a small positive test charge q₀ at a point, measure the force F on it, and divide. Try a different test charge — say, twice as big — and the force doubles, but F/q stays exactly the same. That ratio is a property of the point in space, not of the probe. That’s why we call it a field: a number (and direction) assigned to every point, ready and waiting whether or not anyone comes to measure it.
Two practical notes examiners love. First, the test charge must be tiny (q₀ → 0 in the limit) so it doesn’t disturb the source charges that create the field. Second, the direction of E is, by convention, the direction of the force on a positive charge — a negative charge placed there feels a force in the opposite direction. Keep both facts in mind and half the trick questions in this chapter evaporate.
Field Lines: Drawing the Invisible
Field lines make fields visible. The rules: lines leave + charges and enter − charges; they never cross; where lines are dense the field is strong. The line’s direction at any point is the push a positive test charge would get. A single positive charge radiates outward like a spiky sun; a dipole’s lines arc from + to − like iron filings on paper.
Read the rules carefully, because each one is a statement about physics, not just drawing convention:
- Never crossing: if two lines crossed, the field would have two directions at one point — meaning one test charge pushed two ways at once. Impossible. So a crossing on your diagram is an instant mark-losing error.
- Density = strength: the number of lines passing through a unit area perpendicular to the field is proportional to |E|. Double the line density, double the field.
- Radial spreading: for a point charge, lines spread over a sphere of area 4πr². That growing area is exactly why E falls as 1/r² — geometry writes the inverse-square law.
- Lines are not trajectories: a field line shows the direction of force on a static test charge, not the path a moving charge travels. A charge launched across the lines curves; it does not ride along them.
Superposition: Fields Add as Arrows
Two or more sources? Each point feels every field at once — add them as vectors (arrows head-to-tail, then combine). Two equal positive charges side by side: at the midpoint their fields point oppositely and CANCEL (E = 0 at the centre). A + and − pair (dipole): midpoint fields point the same way and DOUBLE. Always draw the two arrows before adding.
The recipe for every multi-charge problem, in four steps: (1) draw each source’s field arrow at the point, using E = kQ/r² for magnitude and ‘away from +, toward −’ for direction; (2) resolve the arrows into components if they aren’t collinear; (3) add component by component; (4) recombine to get magnitude and direction. This works for two charges, three charges, or a whole ring of charge — the principle never changes, only the bookkeeping.
A bonus worth remembering: at the centre of a uniformly charged ring, or at the centre of a charged spherical shell, symmetry makes all contributions cancel — E = 0. Symmetry arguments can save you minutes of algebra.
Uniform Fields
Between two parallel charged plates, the field lines are parallel, evenly spaced, straight — the uniform field: same strength and direction everywhere inside. E = V/d links it to the voltage across the plates (Part 3). Every oscilloscope and old TV steered electrons with exactly this field.
Why is the field uniform there? Each plate is a large flat sheet whose field is constant (σ/2ε₀ each); between oppositely charged plates the two fields add in the same direction, outside they cancel. The result: a perfectly even field — the closest thing electrostatics has to a level playing field, and the workhorse of every ‘charge in a parallel-plate capacitor’ problem.
Solved Examples
Direct: E = kQ/r² = 9×10⁹ × 3×10⁻⁶ / 0.09 = 3×10⁵ N/C, pointing away (source is +).
Feel it: a 1 C test charge there would be shoved with 300,000 N. ✔
Answer: E = 3×10⁵ N/C, radially outward
Think: near the small charge, its field can match the big one’s. Let the point be x from the 4 μC:
k(4)/x² = k(1)/(0.3−x)² → 2/x = 1/(0.3−x) → x = 0.2 m.
20 cm from the 4 μC charge (10 cm from the 1 μC). The equal-and-opposite point is always nearer the SMALLER charge. ✔
Answer: 20 cm from the 4 μC charge
Both fields point from + toward −: E₊ = kq/(d/2)² away from +; E₋ = kq/(d/2)² toward − — SAME direction.
E = 2 × 4kq/d² = 8kq/d², pointing from + to −.
Contrast: two equal LIKE charges → midpoint E = 0. The dipole doubles; the pair cancels. Draw arrows; never guess. ✔
Answer: E = 8kq/d² along the dipole axis
Step 1: magnitude: F = |q|E = 1.6×10⁻¹⁹ × 5×10⁴ = 8×10⁻¹⁵ N.
Step 2: direction: the electron is negative, so its force is opposite to E — pointing west. ✔
Answer: 8×10⁻¹⁵ N, directed west
- Treating E as a force. E (N/C) belongs to the point in space; F = qE belongs to a specific charge placed there.
- Adding field magnitudes like numbers. Fields add as VECTORS — two equal opposite fields at a point give zero, not double.
- Field lines crossing or starting mid-air. Lines start on +, end on −, never cross (a crossing would mean two pushes at once).
- Using E = kQ/r² for plates or sheets. That’s the point-charge formula only — plates give the uniform V/d field; big flat sheets give σ/2ε₀.
- Forgetting to convert cm to m and μC to C. 30 cm is 0.30 m (squared: 0.09); 3 μC is 3×10⁻⁶ C. Unit slips are the top cause of wrong answers in this chapter.
- Flipping directions for negative charges. E always points away from + and toward −; the force on a negative charge is opposite to E. Keep these two statements separate.
This Physics in Your Daily Life
- Lightning rods work by field shape: the sharp tip concentrates field lines so strongly that air breaks down there first — the strike takes the offered path to ground.
- Photocopier drums and electrostatic precipitators (factory smoke cleaners) steer particles with shaped fields — clean air is applied field lines.
- Old CRT televisions and oscilloscopes steered electron beams with uniform plate fields — the picture you watched was E = V/d in action at 25,000 volts.
- Microwave and radio reception begins with passing radio waves’ fields pushing electrons in your antenna — every bar of signal starts as a field.
- Shielding (Part 5 preview): your phone loses signal in a lift because the metal cage’s fields rearrange — fields, blocked by conductors, in daily life.
- Inkjet printers deflect tiny charged ink droplets between plates — each droplet’s landing spot is set by how long it rides in the uniform field.
Practice set (answers hidden — try first)
(NEET-level) E at 20 cm from a 2 μC charge:
(NEET-level) A 4 μC charge feels 0.8 N in a field. E:
(Concept) Two equal positive charges, midpoint field:
(JEE Main-level) A dipole’s midpoint field direction:
(JEE Main-level) E = 0 between +4q and +q, 1 m apart, is at:
(JEE Main-level) Where is E = 0 for charges +4q and −q placed 1 m apart?
- Therefore, e = F/q · E = kQ/r²
- lines: + → −, dense = strong
- 🔣 E = F/q (definition); E = kQ/r² (point charge)
- In addition, 🔣 field lines: out of +, into −, never cross, dense = strong
- 🔣 superposition: add fields as vectors; opposite equal fields cancel
- 🔣 midpoint: like pair → zero; dipole → doubled along axis
- Therefore, 🔣 uniform field between plates: E = V/d
- 🔁 E = F/q; point charge E = kQ/r²
- 🔁 field lines: never cross; density = strength
- In addition, 🔁 fields superpose as vectors
A charge doesn’t reach out and grab — it modifies the space around it, writing ‘if a + test charge stood here, it would feel THIS push’ at every point. That written instruction is the field. Other charges read the field where THEY stand, not the source.
E = F/q: put a 1 C test charge anywhere and measure. Near a +1 μC point charge at 30 cm: E = 9×10⁹ × 10⁻⁶ / 0.09 = 10⁵ N/C — the same push for any test charge you bring. Double the test charge: force doubles, E unchanged. The field was there before your test arrived.
Picture arrows at every point of space around a positive charge: all pointing radially OUT (positive test charges flee +). Around a negative charge: all pointing IN. Dense arrows = strong field. A dipole’s arrows flow out of + into −, never crossing.
Frequently Asked Questions
- Can E be zero while V is not (or vice versa)? Yes — they are independent quantities. At a dipole’s midpoint E is doubled but V is zero; at the midpoint of two equal like charges E is zero but V is not. Never infer one from the other.
- Is N/C really the same as V/m? Yes. A volt is a joule per coulomb and a joule is a newton-metre, so V/m = (N·m/C)/m = N/C. Exams use both freely.
- Does the field do work on a charge moving perpendicular to it? No. Work needs force along displacement; a charge moving perpendicular to E gains no energy from the field — this fact powers the velocity selector in Part 7.
- Why must the test charge be small? A large test charge would tug on the source charges and rearrange them, changing the very field it came to measure. The limit q₀ → 0 keeps the measurement honest.
- Do field lines ever end in empty space? Never. Every line begins on a positive charge and ends on a negative one (or runs to infinity). A diagram with a dangling line is wrong by definition.
Key Takeaways
- E = F/q defines the field; E = kQ/r² gives it for a point charge — direction: away from +, toward −.
- The field belongs to the point in space, not to any test charge; it exists whether measured or not.
- Therefore, field lines are a picture: out of +, into −, never crossing, denser where stronger.
- Multiple charges: superpose as vectors — like pair cancels at midpoint, dipole doubles.
- Uniform field between plates: parallel evenly-spaced lines, E = V/d.
- 🧠 Chant: ‘lines out of plus, into minus, never crossing’.
- 🧠 Zero-point rule: ‘the neutral spot hides nearer the smaller charge’.
- 🏠 Daily: lightning rods, photocopiers, CRT screens — field-shape engineering.
- 🏠 Daily: phone dead in a lift = fields and conductors, Part 5 preview.
- 🧠 Units: N/C = V/m — both appear in papers; convert freely.
Contents: this page covers Electric Field: The Invisible Influence Around Every Charge with worked notes, tables, a checklist and a rapid recap.
Exam Checklist
- In addition, read once fully, then tables only
- Convert each heading into a question
- Speak five lines aloud as a briefing
- Therefore, index one line in the fortnight sheet
- Return on day three and day seven
FAQ
How much of this page is exam-relevant?
Nearly all of it, because the tables and worked items follow the standard question register for this subject.
When should I revisit?
Day three and day seven after the first read, with the drill spoken aloud once.
The Thirty-Second Recap
One page. One topic. Therefore, read the tables twice. Speak the recap once. Moreover, the numbers carry the marks. The names carry the traps. However, revisits beat rereads. Finally, day three and day seven. That is all.
Explain It Simply
Think of this page as a map of one neighbourhood. The big streets are the tables. The landmarks are the numbers. The street names are the terms in bold. However big the city feels, this one neighbourhood fits in a pocket, and a pocket map is what exam week needs. Therefore, walk it once fully, then walk only the streets you forget, and by the second walk the neighbourhood feels like home.
Pocket the map, not the whole city: exams reward the walkable version of every topic.
Abbreviations That Recur Here
- JEE.
- In addition, nEET.
- ADD.
- CANCEL.
- Therefore, dOUBLE.
- TV.
- SAME.
- In addition, lIKE.
The Plain-Word Walk
Let us walk this page in small words. It began as a long text. Long texts scare readers. However, a map makes them small. Therefore, take the tables as your streets. Walk them once, slow. Then walk them again, fast. The numbers on the walls are your friends. Moreover, the bold words are the street signs. Miss a sign, and you lose your way. However, the walk fixes that too, because the second pass catches what the first pass let slip. In addition, speak one line aloud as you pass each door. A spoken line sticks. A silent line fades. Therefore, the walk ends with a spoken recap, not a closed tab. Finally, the page folds into a pocket map, and exam week loves a pocket map.
Furthermore, the walk has a rule: no new streets on exam eve. However tempting a fresh road looks, the walked streets win. Moreover, your feet know them, and feet beat eyes under a clock. Consequently, the page serves its whole purpose in two walks and one spoken line. Therefore, walk it now. Walk it on day three. Walk it on day seven. Then let the paper ask whatever it wants, because your feet already know the way home.
The Numbers on One Table
| Fact Line | Exam Use |
|---|---|
| The 'changed space' is the electric | Recall anchor |
| Part 2 of the Electrostatics series. | Recall anchor |
| First, the test charge must be tiny (q₀ | Recall anchor |
| Radial spreading: for a point charge, | Recall anchor |
| That growing area is exactly why E | Recall anchor |
The Echo Round
- Numbers to carry: 2 , 8 , 30 , 1 , 12 , 9 , 0 , 4.
- Acronyms to carry: JEE , NEET , ADD , CANCEL , DOUBLE , TV , SAME , LIKE.
- Words worth keeping: anchor, register, corridor, calibration, diligence, threshold, plateau, buffer.
- Walk date one, day three, day seven – the pocket map rule.
Moreover, the echo round exists because retrieval beats rereading, and ten numbers plus eight acronyms, spoken once, outperform an hour of passive scrolling. Therefore, close every revision with this list aloud, and the page banks itself.
Quick revision
- The field is the push a +1 C test charge would feel at a point — it exists even in empty space
- E = F/q (definition) · E = kQ/r² (point charge)
- In addition, field lines: out of +, into −; never cross; denser = stronger
- Multiple charges: fields add as vectors (superposition)
- Uniform field: parallel equally-spaced lines (between plates)
- Therefore, units: N/C = V/m — you will meet both in exams
Have a doubt on this topic?
Sources & official references
External references for fact-checking and further reading.
