NDA Physics · Formula sheet

Electricity and Magnetism formulas

22 formulas, 7 reference tables and 42 common traps for NDA Physics Electricity and Magnetism, grouped by subtopic.

Electrostatics: Charges at Rest

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}

$F$ force between the charges (N)
$q_1, q_2$ the two charges (C)
$r$ separation between them (m)
$k$ Coulomb constant $\approx 9\times10^9$ N·m²/C²

Electric field and field lines

Electric field (definition)

E = \dfrac{F}{q}

$E$ electric field (N/C or V/m)
$F$ force on the test charge (N)
$q$ small positive test charge (C)

Electric potential and potential difference

Potential difference / work

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

$V$ potential difference (volt)
$W$ work done / energy transferred (joule)
$q$ charge moved (coulomb)

Sharp points, corona discharge and lightning protection

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.

Common traps

"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.

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.

"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.

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.

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.

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.

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.

Electric Current and Ohm's Law

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Electric current as rate of flow of charge

Current and charge

I = \dfrac{Q}{t} \quad\Longleftrightarrow\quad Q = I\,t

$I$ current (ampere)
$Q$ charge (coulomb)
$t$ time (second)

Ohm's law — V = IR

Ohm's law

V = I\,R

$V$ potential difference (volt)
$I$ current (ampere)
$R$ resistance (ohm, Ω)

Alternating current vs direct current

Property	DC	AC
Direction	Constant (one way)	Reverses periodically
Source	Cell / battery / DC generator	AC generator / mains
Indian mains frequency	—	50 Hz (reverses every 1/100 s)Q NDA 2024 Sep — mains changes direction every 1/100 s, NOT 1/50 s: a 50 Hz cycle reverses TWICE per cycle.
Transformable?	No (transformers need changing flux)	Yes — step up/down by transformer

Frequency f = 50 Hz ⟹ period T = 1/50 s for a full cycle, but a direction reversal happens every half-cycle = 1/100 s.

Common traps

Convert minutes to seconds first

Q = It needs t in SECONDS. The dominant wrong answer forgets the ×60: 0.6 A × 10 = 6 (using minutes) instead of 0.6 × 600 = 360 C. Always convert time to seconds before multiplying.

Free electrons, not 'both bound and free'

Bound electrons stay with their atoms and don't conduct. The carriers are the FREE electrons only. 'Ions' is correct for solutions/gases, not for a solid metal.

Ohm's law is NOT universal

The false statement the bank tests: 'all homogeneous materials obey Ohm's law irrespective of whether the field is within range or strong.' Wrong — Ohm's law is an empirical approximation that fails for non-ohmic materials and very strong fields.

A rheostat is ohmic; a diode is not

Students wrongly call a rheostat non-ohmic because it 'varies'. It varies the resistance VALUE by sliding a contact, but at any setting it obeys V = IR. The genuine non-ohmic device in the option list is the semiconductor diode.

Reverses every 1/100 s, not 1/50 s

The period of 50 Hz AC is 1/50 s — but that is one FULL cycle, which contains TWO reversals. The current changes direction every half-period = 1/100 s. Picking 1/50 s is the dominant trap.

Resistance and Resistivity

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Resistance and what controls it

Resistance of a uniform wire

R = \rho\,\dfrac{L}{A}

$R$ resistance (Ω)
$\rho$ resistivity of the material (Ω·m)
$L$ length of the wire (m)
$A$ cross-sectional area (m²)

Stretching and cutting a wire

Stretched wire (constant volume)

R' = k^2 R \quad\text{when length}\to kL,\ \text{area}\to A/k

$k$ factor by which the length increases
$R'$ new resistance after stretching
$R$ original resistance

Common traps

Current does not affect resistance

R is a property of the conductor (material + geometry), set before any current flows. The trap option 'the current through it' is exactly what does NOT change R for an ohmic resistor.

Stretching changes R, not ρ

A wire stretched longer has more resistance, but its resistivity is unchanged — same material, same temperature. The distractors 'doubled/halved' tempt you to treat ρ like R. ρ is intrinsic; it doesn't care about shape.

Stretching is R ∝ L², not R ∝ L

Forgetting that the wire also gets THINNER is the classic error. Volume is fixed, so doubling length halves area, and R = ρL/A picks up BOTH factors: ×2 from length and ×2 from area = ×4 overall. Use R ∝ L².

Combination of Resistors

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Resistors in series

Series equivalent

R_\text{series} = R_1 + R_2 + \cdots + R_n

Resistors in parallel

Parallel equivalent

\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots \qquad (\text{two: } R = \tfrac{R_1R_2}{R_1+R_2})

Cutting a wire and reconnecting it

Cut into n, reconnect in parallel

R_\text{final} = \dfrac{R}{n^2}

Common traps

Series = same current, voltages add

Don't confuse the two combinations. Series: one current path, add the resistances. The combination can never be smaller than any single resistor in it.

Parallel value is SMALLER than the smallest branch

If you compute a parallel combination and get something bigger than one of the branches, you've made an error. Adding paths reduces resistance. For two equal R the answer is R/2, never 2R.

Collapse innermost first — don't add everything blindly

You can't add a series and a parallel resistor in one step. Identify a sub-group that is PURELY one kind, reduce it, redraw, and only then look at the next group. Mixing the two rules in a single step is the most common network error.

Cut + parallel = R/n², not R/n

Two effects stack: cutting into n pieces makes each R/n, AND paralleling n of them divides by another n. The combined result is R/n². Stopping at R/n is the dominant wrong answer.

Minimum ≠ fewest resistors

Minimum resistance means MOST parallel paths of the SMALLEST resistors — not the smallest count of components. Three 3 Ω in parallel (1 Ω) beats two 1 Ω in series (2 Ω): more parallelism wins even with larger individual values.

Electrical Power, Energy and Heating

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Electrical power — three equivalent forms

Electrical power

P = VI = I^2 R = \dfrac{V^2}{R}

$P$ power (watt)
$V$ voltage (volt)
$I$ current (ampere)
$R$ resistance (ohm)

Power rating and running at the wrong voltage

Power vs voltage at fixed R

P = \dfrac{V^2}{R}, \quad R = \dfrac{V_0^2}{P_0} \;\Rightarrow\; \dfrac{P}{P_0} = \left(\dfrac{V}{V_0}\right)^2

Electrical energy and the cost of running appliances

Energy and cost

E\,(\text{kWh}) = P\,(\text{kW}) \times t\,(\text{h}), \qquad \text{Cost} = E \times \text{rate}

Joule heating — current heats a resistor

Joule heating

H = I^2 R\,t = V I t = \dfrac{V^2}{R}\,t

$H$ heat produced (joule)
$I$ current (A)
$R$ resistance (Ω)
$t$ time (s)

Common traps

I²R is power; IR² and I²/R are not

The bank tests this by dimensions. P = I²R ✓ and P = V²/R ✓. But IR² and I²/R are NOT power — check by substituting V = IR if unsure. Memorise the three valid forms and spot the impostor.

Power scales as V², not V

Running a bulb at half voltage does NOT halve the power — it quarters it. The resistance is fixed by the rating, so P = V²/R falls with the square of the voltage. Picking 40 W (half) instead of 20 W (quarter) is the standard trap.

Keep power in kW and time in hours

kWh = kW × hours. Don't convert power to watts or time to seconds for billing problems — that buries you in 10⁶ factors. Units × rate per unit gives the cost directly.

Heat depends on all of V, I, and t

Multi-statement questions try to drop one factor. H = VIt contains voltage, current, AND time — the temperature rise needs all three. Don't select 'current and time only'.

Same VOLTAGE → use V²/R; don't reach for I²R

When the two arrangements share the same applied voltage, power is V²/R, so smaller resistance means more heat (parallel wins). Reaching for I²R here misleads, because the current is different in each arrangement. The ratio is 4 : 1, and picking the inverted 1 : 4 is the dominant trap.

Cells, EMF and Kirchhoff's Laws

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EMF, internal resistance and terminal voltage

Terminal voltage and circuit current

V = \varepsilon - I r, \qquad I = \dfrac{\varepsilon}{R + r}

$\varepsilon$ EMF of the cell (volt)
$r$ internal resistance (Ω)
$R$ external resistance (Ω)
$V$ terminal voltage (volt)

Kirchhoff's two laws

Kirchhoff's laws

\sum_\text{junction} I = 0, \qquad \sum_\text{loop} (\varepsilon - IR) = 0

Common traps

Terminal voltage drops as current rises

EMF is fixed, but the terminal voltage V = ε − Ir falls as the cell delivers more current. A heavily loaded battery (large I) shows a noticeably lower terminal voltage — that's the internal resistance at work.

Loop rule = energy; junction rule = charge

Don't mix them up. The LOOP (voltage) rule comes from energy conservation; the JUNCTION (current) rule comes from charge conservation. The distractors 'Ohm's law' and 'conservation of momentum' are both wrong for the loop rule.

Parallel bulbs each get full voltage — series bulbs split it

More cells in series AND bulbs in parallel both raise the voltage across each bulb. The brightest arrangement maximises per-bulb voltage: two cells in series feeding bulbs in parallel beats any series-bulb arrangement.

Magnetism and Magnetic Effects of Current

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Magnetic field of a current-carrying straight wire

Field of a straight wire

B = \dfrac{\mu_0 I}{2\pi r}

$B$ magnetic field (tesla)
$I$ current in the wire (A)
$r$ perpendicular distance from the wire (m)
$\mu_0$ permeability of free space

Magnetic field of a solenoid

Field inside a solenoid

B = \mu_0 n I

$B$ field inside the solenoid (T)
$n$ turns per unit length (per m)
$I$ current (A)

Magnetic field at the centre of a circular coil

Field at centre of a coil

B = \dfrac{\mu_0 N I}{2R}

$N$ number of turns
$I$ current (A)
$R$ radius of the coil (m)

Magnetic materials — what a magnet attracts

Class	Behaviour	Examples
Ferromagnetic	Strongly attracted; can be magnetised	Iron, nickel, cobalt, steel (incl. many stainless steels)
Paramagnetic	Very weakly attracted	Aluminium, platinum, manganese
Diamagnetic / non-magnetic	Not attracted (very weakly repelled)	Plastic, carbon, copper, glass, water

A magnet strongly attracts only ferromagnetic materials; plastic and carbon are non-magnetic.

Common traps

Field lines are CLOSED and exist INSIDE the magnet

Two favourite false statements: 'magnetic field lines are open curves' (wrong — they're closed) and 'there are no field lines within a bar magnet' (wrong — they run S→N inside). Both are the answers to 'which is NOT correct'.

Magnetic EQUATOR, not magnetic meridian

The field is horizontal at the magnetic equator. 'Magnetic meridian' (the vertical plane containing the needle) and 'geographic pole' are distractors — the equator is where dip = 0.

Stainless steel is (usually) magnetic; aluminium is only weakly so

Common stainless steels contain iron and ARE attracted by a magnet. Aluminium is paramagnetic — weakly attracted, which the bank counts as 'attracted'. Plastic and carbon are not. That gives 2 of the 4.

Depends on current and distance — not on the wire's radius

The field outside a straight wire depends on the current and your distance from the axis, NOT on the wire's own thickness or the surrounding temperature. B ∝ I and B ∝ 1/r.

Field depends on turns-per-length and current, not diameter

B = μ₀nI: only n and I matter. A common false statement is 'inserting a soft-iron bar leaves the field unchanged' — wrong, the core boosts it sharply. Another distractor adds the diameter as a dependence — it isn't one.

Combine the factors: N up AND R down both raise B

B ∝ N/R. Doubling N gives ×2; halving R gives another ×2; together ×4. Forgetting one factor (answering 0.2 T) is the dominant trap.

Magnetic Force and Fleming's Rules

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Force on a charge moving in a magnetic field

Magnetic force on a moving charge

F = qvB\sin\theta

$q$ charge (C)
$v$ speed (m/s)
$B$ magnetic field (T)
$\theta$ angle between v and B

Force on a current-carrying conductor — Fleming's left-hand rule

Force on a current-carrying conductor

F = B I L

$F$ force (N)
$B$ magnetic field (T)
$I$ current (A)
$L$ length of conductor in the field (m)

Common traps

No force when motion is ALONG (or against) the field

Both θ = 0° and θ = 180° give sinθ = 0, so a charge moving parallel OR antiparallel to B feels no magnetic force. 'Moving south, field north' is the antiparallel case — the answer is no deflecting force, not a sideways one.

LEFT hand for force (motor), not right

Fleming's LEFT-hand rule gives the FORCE on a current (motor effect). The right-hand rule is for the current INDUCED by motion (generator). The distractor 'right-hand rule' is the classic swap.

Right hand → induced current (generator)

Keep the pair straight: LEFT hand = force on a current (motor), RIGHT hand = current induced by motion (generator). Here forefinger = field and thumb = motion, so the middle finger gives the INDUCED CURRENT — not 'force' and not 'electric field'.

Electrical Devices and Safety

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Transformers — changing AC voltage

Transformer turns ratio

\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p}

$V_p, V_s$ primary / secondary voltage
$N_p, N_s$ primary / secondary turns

Heating elements and bulb filaments

Device / part	Material	Why
Heating element (iron, heater, toaster)	Nichrome	High resistivity (heats well) + high melting point + doesn't oxidiseQ
Incandescent bulb filament	Tungsten	Highest melting point (~3400°C) — glows white-hot without meltingQ
Photoelectric cell	Rubidium / caesium	Alkali metals have a low work function — emit electrons easily under lightQ NDA 2018 Apr — photo-cell metal is rubidium (an alkali metal), NOT tungsten or copper.

Nichrome HEATS, tungsten LIGHTS, alkali metals (rubidium/caesium) EMIT electrons in photocells.

Fuses, earthing and household wiring

Item	Key fact
Fuse wire	Conducting, low melting point; in SERIES — melts and breaks the circuit on excess currentQ
Short circuit	Resistance drops near zero ⟹ current increases substantially (which is what blows the fuse)Q
Three-wire colour code	Red = live, Green = earth (ground), Black = neutralQ NDA 2018 Sep — the OLD Indian code: red live, green earth, black neutral (don't confuse with newer brown/green-yellow/blue).

A fault ⟹ large current ⟹ the low-melting-point fuse melts first, protecting the rest of the circuit.

Generators, motors and the AC/DC distinction

Device / question	Answer
Generator / dynamo works on…	Faraday's law of electromagnetic inductionQ
Device used to produce electric current	Generator (a motor consumes current; a galvanometer detects it)Q
Convert an AC generator to DC	Replace slip rings with a split-ring commutatorQ NDA 2023 Sep — slip rings ⟹ AC output; a split-ring commutator ⟹ DC output. That ring is the only change.

Generator = motion → current (induction). Motor = current → motion. Commutator (split-ring) = the AC→DC converter.

Meters, conductors and insulators

Instrument / term	Connection	Key property
Ammeter	In series	Low resistance (so it doesn't reduce the current)
Voltmeter	In parallel	High resistance (so it draws almost no current)Q NDA 2025 Apr — the WRONG statement is 'voltmeter low resistance, ammeter high resistance' — it's the reverse.
Galvanometer	—	Detects the presence of current in a circuitQ
Insulator	—	Electrons do NOT flow through it easily (few free electrons)Q

Ammeter: series + low R. Voltmeter: parallel + high R. Galvanometer: detects current. Insulator: electrons can't flow easily.

Common traps

Nichrome heats, tungsten lights — don't swap them

Tungsten's selling point is its melting point (for a glowing filament); nichrome's is high resistivity with durability (for a heater). Swapping the two metals is the standard distractor.

Fuse = LOW melting point (and conducting)

A fuse must conduct normally but melt easily on overload, so it needs a LOW melting point. 'High melting point' and 'insulator' are both wrong — an insulator wouldn't carry the normal current at all.

Generator produces current; motor consumes it

A motor runs ON current (it doesn't produce it); a galvanometer DETECTS current. The device that PRODUCES current is the generator. And the AC↔DC switch is purely the slip-ring vs split-ring choice.

Transformers change VOLTAGE, not power — and need AC

A step-up transformer raises voltage (and lowers current); it does NOT 'increase electrical power'. And it works only on AC. The distractors 'increases power' and any DC use are wrong.

Voltmeter HIGH resistance, ammeter LOW — the common swap

The false statement to catch: 'a voltmeter has low resistance and an ammeter has high resistance.' It's reversed. Voltmeter = high R (parallel); ammeter = low R (series).

Electricity and Magnetism formulas

Electrostatics: Charges at Rest

Coulomb's law — force between two charges

Electric field and field lines

Electric potential and potential difference

Sharp points, corona discharge and lightning protection

Common traps

Electric Current and Ohm's Law

Electric current as rate of flow of charge

Ohm's law — V = IR

Alternating current vs direct current

Common traps

Resistance and Resistivity

Resistance and what controls it

Stretching and cutting a wire

Common traps

Combination of Resistors

Resistors in series

Resistors in parallel

Cutting a wire and reconnecting it

Common traps

Electrical Power, Energy and Heating

Electrical power — three equivalent forms

Power rating and running at the wrong voltage

Electrical energy and the cost of running appliances

Joule heating — current heats a resistor

Common traps

Cells, EMF and Kirchhoff's Laws

EMF, internal resistance and terminal voltage

Kirchhoff's two laws

Common traps

Magnetism and Magnetic Effects of Current

Magnetic field of a current-carrying straight wire

Magnetic field of a solenoid

Magnetic field at the centre of a circular coil

Magnetic materials — what a magnet attracts

Common traps

Magnetic Force and Fleming's Rules

Force on a charge moving in a magnetic field

Force on a current-carrying conductor — Fleming's left-hand rule

Common traps

Electrical Devices and Safety

Transformers — changing AC voltage

Heating elements and bulb filaments

Fuses, earthing and household wiring

Generators, motors and the AC/DC distinction

Meters, conductors and insulators

Common traps

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