NDA Physics · Electricity and Magnetism

Electrostatics: Charges at Rest

Electric charge is a conserved, quantised property of matter; charges at rest exert forces (Coulomb's law), set up an electric field and potential, and arrange themselves on conductor surfaces so the inside stays field-free.

All Electricity and Magnetism notes NDA Physics strategy

Why this matters

Electrostatics opens the chapter — 13 PYQs, mostly EASY/MODERATE, and the conceptual bedrock for everything that follows. Three families dominate: (1) properties of charge + how things get charged (friction, induction), (2) the field/potential pair — field lines point away from +charge, V = W/q, (3) conductor behaviour — why the inside of a metal shell is field-free, and why a lightning rod is pointed. The questions reward clean definitions, not heavy maths.

Concept 1 of 7

Electric charge and its three properties

Intuition

Charge is the property of matter that makes it feel electric force. It comes in two signs (positive, negative), and at the everyday level it behaves like a bookkeeping quantity: you can move it around, but you can never make it appear from nothing or vanish into nothing.

Definition

Electric charge has three NDA-tested properties:

Quantised — charge is always an integer multiple of the elementary charge $e = 1.6\times10^{-19}$ C, so $q = ne$ . You cannot have half an electron's worth of charge.
Conserved — the total charge of an isolated system never changes. Charging is always TRANSFER, never creation.
Additive — the net charge of a body is the algebraic sum (with sign) of all the charges on it.

Worked example

A body carries a charge of

-3.2\times10^{-19}

C. How many excess electrons does it hold?

Charge is quantised: $q = ne$ , so $n = q/e$ .
$n = \dfrac{3.2\times10^{-19}}{1.6\times10^{-19}} = 2$ .
The negative sign means the EXCESS particles are electrons (not a fractional or positive count).

Answer:2 excess electrons.

Practice this conceptself-check · 3 quick reps

Try it yourself

Two identical metal spheres carry +6 C and −2 C. They are touched together and separated. What charge does each now carry, and which property guarantees it?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Charge on a body is always an integer multiple of what?
2.
Can charge be created or destroyed in an isolated system?
3.
A body has 5 excess electrons. What is its charge?

From the bank · past-year question

Example 1Electricity and MagnetismEASY

Which one of the following is NOT a basic property of electric charge?

[Q135 · Apr · 2025]

"Charges can be created and destroyed" is the WRONG option

Conservation forbids it — charge is only ever transferred. NDA phrases the question as "which is NOT a property of charge", and the create/destroy line is the answer. Don't confuse charging (transfer) with creation.

Concept 2 of 7

How objects get charged — friction and induction

Intuition

Rubbing two insulators transfers electrons from one to the other: the body that GAINS electrons becomes negative, the one that LOSES them becomes positive. No protons move — only the light, mobile electrons. Induction charges a body without contact by letting a nearby charge rearrange its electrons.

Definition

Charging by friction — rubbing transfers electrons. The material with weaker hold on electrons loses them (turns +); the other gains them (turns −). Equal and opposite charge appears, conserving total charge.
Charging by induction — bringing a charge near a conductor (without touching) pulls opposite charge to the near face and pushes like charge to the far face; grounding the far face then leaves a net charge.
Insulators hold static charge — charge sprayed onto an insulator stays put (electrons can't flow away), which is exactly why static electricity is an insulator phenomenon.

Worked example

A glass rod is rubbed with silk and becomes positively charged. What happened to the electrons, and what is the silk's charge?

Charging by friction transfers electrons, never protons.
Glass turned positive ⟹ glass LOST electrons.
By conservation, those electrons went onto the silk ⟹ silk gained electrons ⟹ silk is negative.

Answer:Electrons moved from glass to silk; the silk is negatively charged.

Practice this conceptself-check · 3 quick reps

Try it yourself

A positively charged rod is brought near (but not touching) an isolated metal sphere. Describe the charge on the near and far faces of the sphere while the rod is held there.

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
A rod rubbed with wool becomes negative. Which way did electrons move?
2.
What kind of material can hold static charge?
3.
In charging by friction, do protons ever transfer?

From the bank · past-year question

Example 2Electricity and MagnetismEASY

Suppose a rod is given a negative charge by rubbing it with wool. Which one of the following statements is correct in this case ?

[Q119 · Apr · 2017]

Only electrons move — never protons

Protons are locked in the nucleus. A body turns positive by LOSING electrons, not by gaining protons. Options that say "positive charges transferred" are wrong unless they're describing the net effect, not the actual carriers.

Drill 2 more on how objects get charged — friction and induction

Concept 3 of 7

Coulomb's law — force between two charges

Intuition

Two charges push or pull along the line joining them. Like signs repel, unlike signs attract, and the force weakens fast with distance — quartering when you double the separation (inverse-square).

Definition

The electrostatic force between two point charges is like charges repel, unlike charges attract, directed along the line joining them. Doubling the distance cuts the force to a quarter (inverse-square). A "positive" (repulsive) force means the two charges have the SAME sign.

Coulomb's law

F = \dfrac{1}{4\pi\varepsilon_0}\,\dfrac{q_1 q_2}{r^2} = k\,\dfrac{q_1 q_2}{r^2}

Fforce between the charges (N)
q_1, q_2the two charges (C)
rseparation between them (m)
kCoulomb constant $\approx 9\times10^9$ N·m²/C²

Worked example

Two charges repel with force

F

. Without changing the charges, the distance between them is doubled. What is the new force?

Coulomb's law: $F \propto 1/r^2$ at fixed charges.
Doubling $r$ makes $r^2$ four times larger.
So the force becomes $F/4$ .

Answer:F/4 — the force is still repulsive (same signs), just one-quarter as strong.

Practice this conceptself-check · 3 quick reps

Try it yourself

Charge A repels charge B, and B repels charge C. What can you say about the signs of A and C?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Two like charges experience what kind of force?
2.
If the distance between two fixed charges is halved, the force becomes…
3.
A 'positive' (repulsive) force tells you the two charges are…

From the bank · past-year question

Example 3Electricity and MagnetismMODERATE

Which of the following statements correctly explains/explain the existence of a positive force between two electric charges? 1. Both the charges are positive. 2. Both the charges are negative. 3. Both the charges are oppositely charged. Select the correct answer using the code given below.

[Q54 · Apr · 2022]

"Positive force" = repulsion = like charges

The bank uses "positive force" to mean repulsion. That happens for BOTH-positive AND BOTH-negative pairs (statements 1 and 2), not for opposite charges. The opposite-charge case gives an attractive (negative) force.

Concept 4 of 7

Electric field and field lines

Intuition

Every charge fills the space around it with an electric field — a force-per-unit-charge that a test charge would feel. We draw the field as lines: they start on positive charge and end on negative charge, and the arrow shows the force on a positive test charge.

Definition

The electric field $E = F/q$ is the force per unit positive test charge (N/C). Field-line rules:

Lines start on positive charge, end on negative charge; they never cross.
At a conductor surface the field is perpendicular to the surface (any parallel component would push the surface charges until it vanished).
Around an isolated positively charged sphere the lines are radial and outward; for a negative sphere, radial and inward.

Electric field (definition)

E = \dfrac{F}{q}

Eelectric field (N/C or V/m)
Fforce on the test charge (N)
qsmall positive test charge (C)

Field lines start on positive charge, end on negative, and meet a sphere radially (perpendicular to its surface).

Worked example

A test charge of

2\times10^{-6}

C placed at a point feels a force of

4\times10^{-3}

N. What is the electric field there?

Field is force per unit charge: $E = F/q$ .
$E = \dfrac{4\times10^{-3}}{2\times10^{-6}} = 2\times10^{3}$ N/C.
It points along the force (the test charge is positive).

Answer:E = 2×10³ N/C, directed along the force.

Practice this conceptself-check · 4 quick reps

Try it yourself

Why must electric field lines meet the surface of a charged conductor at right angles?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Field lines start on which charge and end on which?
2.
Field lines from an isolated positive sphere point…
3.
At a conductor's surface, the electrostatic field is…
4.
Can two electric field lines cross?

From the bank · past-year question

Example 4Electricity and MagnetismMODERATE

The electric field lines from an isolated positively charged conducting sphere are

[Q56 · Apr · 2022]

Outward AND perpendicular — both words matter

For a positive conducting sphere the distractors offer "tangential" (wrong — must be perpendicular) and "towards the centre" (wrong direction — that's a negative sphere). The right answer is perpendicular to the surface AND directed outward.

Concept 5 of 7

Electric potential and potential difference

Intuition

Potential is electrical 'height' — the work needed to bring one unit of positive charge to a point. Potential DIFFERENCE between two points is the work per unit charge to move between them; that is exactly what a voltmeter reads.

Definition

Potential difference $V = W/q$ is the work done per unit charge in moving a charge between two points (unit: volt = joule/coulomb). Moving a charge $q$ through a PD $V$ changes its energy by $W = qV$ . The electron-volt (eV) is the energy an electron gains across 1 volt: $1\text{ eV} = 1.6\times10^{-19}$ J.

Potential difference / work

V = \dfrac{W}{q} \quad\Longleftrightarrow\quad W = qV

Vpotential difference (volt)
Wwork done / energy transferred (joule)
qcharge moved (coulomb)

Worked example

Moving a charge of 5 C between two points takes 100 J of work. What is the potential difference between the points?

Potential difference is work per unit charge: $V = W/q$ .
$V = \dfrac{100}{5} = 20$ V.

Answer:20 V.

Practice this conceptself-check · 3 quick reps

Try it yourself

An electron is accelerated through a potential difference of 500 V. How much energy (in joules) does it gain?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
What is the SI unit of potential difference?
2.
Work to move 2 C through 6 V?
3.
Energy gained by an electron crossing 1 kV, in joules?

From the bank · past-year question

Example 5Electricity and MagnetismEASY

The work done in moving a charge of 2 coulomb (C) from point A to point B is 24 J. What is the potential difference between A and B?

[Q127 · Apr · 2025]

Divide work by charge — don't multiply

For "work W to move charge q, find PD", the answer is

V = W/q

. The distractor multiplies (W×q) or inverts the ratio. Units settle it: volts = joules ÷ coulombs.

Drill 1 more on electric potential and potential difference

Concept 6 of 7

Conductors in electrostatics — field-free interior

Intuition

Give a conductor some charge and its free electrons rearrange in an instant until no field is left inside the metal. All the excess charge sits on the OUTER surface, and the cavity inside a hollow conductor is completely shielded from outside fields — the principle behind a Faraday cage.

Definition

In static equilibrium on a conductor:

The electric field inside the conducting material is zero — free charges move until it is.
All excess charge resides on the outer surface.
A hollow conductor shields its cavity from external fields (Faraday cage / electrostatic shielding).

For a charge $+q$ at the centre of a hollow metal shell (inner radius $a$ , outer $b$ ): the field is non-zero for $r<a$ , zero within the metal $a<r<b$ , and non-zero again outside.

Worked example

Why does a car act as a relatively safe place during a lightning strike, even though the body is metal?

A car body is a (roughly) closed conductor.
Charge from a strike spreads over the OUTER metal surface.
The electric field inside the conducting shell stays zero — the cavity is shielded.
So the occupants inside are protected — this is electrostatic shielding (a Faraday cage).

Answer:The metal shell carries the charge on its outside and keeps the interior field-free (Faraday-cage shielding).

Practice this conceptself-check · 3 quick reps

Try it yourself

A solid metal sphere is given a charge Q. Where does the charge sit, and what is the field deep inside the metal?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Electric field inside the material of a charged conductor?
2.
Where does excess charge on a conductor reside?
3.
What protects the cavity of a hollow conductor from outside fields?

From the bank · past-year question

Example 6Electricity and MagnetismHARD

A positive charge

+q

is placed at the centre of a hollow metallic sphere of inner radius

a

and outer radius

b

. The electric field at a distance

r

from the centre is denoted by

E

. In this regard, which one of the following statements is correct ?

[Q143 · Apr · 2017]

Field is zero INSIDE THE METAL (a<r<b), not everywhere

For a central charge in a hollow shell, the field is zero only within the conducting material

a<r<b

. Between the charge and the inner wall (

r<a

) and outside the shell (

r>b

) the field is non-zero. Don't over-extend the 'field is zero' rule.

Concept 7 of 7

Sharp points, corona discharge and lightning protection

Intuition

Charge crowds onto the sharpest parts of a conductor, making the field there enormous. That intense field ionises the surrounding air into a 'corona' that quietly bleeds charge away — which is exactly why a lightning rod is pointed and why aircraft tyres are made conducting.

Definition

Charge density (and hence field) is largest where a conductor is most sharply curved — a pointed tip. The strong field there drives corona discharge, continuously leaking charge to/from the air. This is the recall cluster the bank tests as applications.

Situation	Reason
Lightning rod has a pointed tip	Sharp point ⟹ very high field ⟹ continuous corona discharge that neutralises charge before a strike buildsQ
Lightning itself	Flow of charge between oppositely charged regions of cloud/ground once the field exceeds air's breakdownQ
Aircraft tyres made of conducting rubber	Lets charge built up in flight (by friction with air, by onboard electronics) drain harmlessly to ground on landingQ
Why pointed, not spherical/flat	A pointed top concentrates the most charge ⟹ strongest discharge action; a sphere or flat block would notQ NDA 2026 Apr — a sharp tip works by ENHANCING the local field to promote corona discharge, not by reducing it.

All four reduce to one idea: charge concentrates at sharp points, raising the field enough to discharge through the air.

Practice this conceptself-check · 3 quick reps

Try it yourself

Two identical conductors carry the same charge — one is a smooth sphere, the other has a sharp spike. Near which does the air break down (spark) first, and why?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Best shape for the tip of a lightning conductor?
2.
What is the discharge of charge from a sharp point into the air called?
3.
Why are aircraft tyres made of conducting rubber?

From the bank · past-year question

Example 7Electricity and MagnetismMODERATE

Which one of the following is the best shape of a solid metal rod to form the top end of a lightning conductor ?

[Q54 · Apr · 2024]

A sharp tip ENHANCES the field — it doesn't reduce it

The 2026 question offers "the sharp tip reduces the local field" as a distractor. Backwards. A sharp point INTENSIFIES the field, which is what drives the protective corona discharge.

Drill 3 more on sharp points, corona discharge and lightning protection

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Coulomb's law — force between two charges
Coulomb's law
$F = \dfrac{1}{4\pi\varepsilon_0}\,\dfrac{q_1 q_2}{r^2} = k\,\dfrac{q_1 q_2}{r^2}$
Electric field and field lines
Electric field (definition)
$E = \dfrac{F}{q}$
Electric potential and potential difference
Potential difference / work
$V = \dfrac{W}{q} \quad\Longleftrightarrow\quad W = qV$

Reference tables (1)

Sharp points, corona discharge and lightning protection4 rows

Situation	Reason
Lightning rod has a pointed tip	Sharp point ⟹ very high field ⟹ continuous corona discharge that neutralises charge before a strike buildsQ
Lightning itself	Flow of charge between oppositely charged regions of cloud/ground once the field exceeds air's breakdownQ
Aircraft tyres made of conducting rubber	Lets charge built up in flight (by friction with air, by onboard electronics) drain harmlessly to ground on landingQ
Why pointed, not spherical/flat	A pointed top concentrates the most charge ⟹ strongest discharge action; a sphere or flat block would notQ NDA 2026 Apr — a sharp tip works by ENHANCING the local field to promote corona discharge, not by reducing it.

All four reduce to one idea: charge concentrates at sharp points, raising the field enough to discharge through the air.

Watch out for (7)

"Charges can be created and destroyed" is the WRONG option
→ Electric charge and its three properties
Only electrons move — never protons
→ How objects get charged — friction and induction
"Positive force" = repulsion = like charges
→ Coulomb's law — force between two charges
Outward AND perpendicular — both words matter
→ Electric field and field lines
Divide work by charge — don't multiply
→ Electric potential and potential difference
Field is zero INSIDE THE METAL (a<r<b), not everywhere
→ Conductors in electrostatics — field-free interior
A sharp tip ENHANCES the field — it doesn't reduce it
→ Sharp points, corona discharge and lightning protection

Mastery check — 5 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Electricity and MagnetismEASY

Which one of the following can charge an insulator?

[Q77 · Apr · 2019]

Example 2Electricity and MagnetismMODERATE

If a free electron moves through a potential difference of 1 kV, then the energy gained by the electron is given by

[Q72 · Sep · 2018]

Example 3Electricity and MagnetismMODERATE

Lightning is due to

[Q68 · Sep · 2024]

Example 4Electricity and MagnetismMODERATE

For a material under static conditions, which one among the following statements is correct ?

[Q72 · Sep · 2025]

Example 5Electricity and MagnetismMODERATE

Why are the tyres of aircrafts made of conducting rubber? 1. So that the charge accumulated on the aircraft in flight, by rubbing the air, can easily be transferred to ground on landing. 2. So that the charge accumulated due to the operation of various electronic equipments in the aircraft in flight can easily be transferred to ground on landing. Select the correct answer using the code given below.

[Q100 · Apr · 2022]

Drill every past-year question on this subtopic

13 questions from the bank — paginated, with cart and Word-export support.

Drill the 13 questions