Electrostatics Formula Sheet — NEET Physics

Every key Electrostatics formula, definition and fact for NEET Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNCERT · 5 sub-topics

Electric charge, Coulomb’s law, electric field & field lines
Electric dipole, electric flux, Gauss’s law & applications
Electric potential & potential difference, equipotential surfaces
Conductors, dielectrics & polarisation, capacitors & combinations
Energy stored in a capacitor

Electric Charge & Coulomb's Law

Properties of charge

▸ $Quantised$ : $Q = \pm n e$ ( $e = 1.6 \times 1 0^{- 19}$ C).
▸ $Conserved$ and $additive$ (algebraic, scalar).
▸Relativistically $invariant$ (independent of frame/speed).
▸Conductors have free electrons; insulators do not.

Coulomb's law

F = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r ^{2}} = k \frac{q _{1} q _{2}}{r ^{2}}

k = 9 \times 1 0^{9} N m^{2} C^{- 2}

ε_{0} = 8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}

;

r =

separation

In a medium

F_{m e d} = \frac{F _{v a c}}{K} = \frac{1}{4 π ε _{0} K} \frac{q _{1} q _{2}}{r ^{2}}

K = ε_{r} =

dielectric constant of the medium (

K = 1

vacuum)

Two like charges separated by r repelling each other along the line joining them — Like charges repel, unlike attract — along the line joining.

Comparative: Coulomb vs gravitation

	Coulomb	Gravitation
Law	$k q_{1} q_{2} / r^{2}$	$G m_{1} m_{2} / r^{2}$
Sign	$\pm$ (attract/repel)	always attractive
Strength	$\sim 1 0^{39} \times$ stronger	weaker
Medium-dependent?	yes ( $/ K$ )	no

⚡ Shortcut · Superposition

Net force

F = \sum_{i} F_{i}

— each pair's Coulomb force is computed as if the others were absent, then added as

vectors

. For three charges in a line, watch the directions before summing magnitudes.

🚫 Examiner Trap · Charge & Coulomb's law

(1) r is the

separation

between charges (centre-to-centre for spheres), not a coordinate. (2) In a medium, force drops by K — don't forget it. (3) Add forces as

vectors

, never scalar magnitudes. (4) Charge is quantised (

Q = n e

) and conserved — a body can't carry a fractional e.

Electric Field & Field Lines

Electric field

E

: Force per unit positive test charge

E = \frac{F}{q _{0}}

(in the limit

q_{0} \to 0

); point charge

E = \frac{k q}{r ^{2}}

. Unit N C

^{- 1} =

m^{- 1}

. Obeys superposition

E = \sum E_{i}

Comparative: field of standard bodies

Body	$E$	Note
Point charge	$k q / r^{2}$	radial
Ring (axis)	$\frac{k Q x}{( x ^{2} + R ^{2} ) ^{3/2}}$	max at $x = R / 2$
Shell / sphere (out)	$k Q / r^{2}$	like point charge
Shell inside / solid inside	$0 / kQr / R^{3}$	—
Infinite wire	$\frac{λ}{2 π ε _{0} r}$	$\propto 1/ r$
Infinite sheet	$\frac{σ}{2 ε _{0}}$	uniform

Field lines of a positive charge (outward), negative charge (inward), a dipole, and two like charges with a null point — Field-line patterns.

Field-line properties

▸Start at $+$ , end at $-$ ; never form closed loops (electrostatic field is conservative).
▸Tangent gives $E$ direction; line density $\propto ∣ E ∣$ .
▸Two lines never cross; meet a conductor $⊥$ ; none inside a conductor.

🚫 Examiner Trap · Electric field & lines

(1) Isolated sheet gives

\frac{σ}{2 ε _{0}}

, but a

conductor

surface gives

\frac{σ}{ε _{0}}

(twice) — don't confuse. (2)

E = 0

inside

a uniform shell, but

V \neq = 0

there. (3) Field lines never cross and never close on themselves. (4) E is max on a ring's axis at

x = R / 2

not

at the centre (

E_{ce n t re} = 0

Electric Dipole & Gauss's Law

Dipole field

p = q (2 a); E_{a x ia l} = \frac{2 k p}{r ^{3}}, E_{e q u a t or ia l} = \frac{k p}{r ^{3}}

p

points

-

+

; general

E = \frac{k p}{r ^{3}} 1 + 3 cos^{2} θ

for

r ≫ a

Torque & energy

τ = p \times E (τ = pE sin θ); U = - p \cdot E

θ =

angle between

p

and

E

; stable at

θ = 0

, unstable at

18 0^{\circ}

; no net force in a

uniform

field

Comparative: axial vs equatorial

	Axial	Equatorial
Field $E$	$2 k p / r^{3}$	$k p / r^{3}$
Direction	along $p$	opposite $p$
Potential $V$	$k p / r^{2}$	$0$

Gauss's law

Φ = \oint E \cdot d A = \frac{q _{e n c}}{ε _{0}}

net flux depends

only

on enclosed charge, not on its position or outside charges

A point charge enclosed by a spherical Gaussian surface with radial field lines passing through it — Total flux $= q / ε_{0}$ .

Gauss applications

E_{w i re} = \frac{λ}{2 π ε _{0} r}, E_{s h ee t} = \frac{σ}{2 ε _{0}}, E_{co n d u c t or} = \frac{σ}{ε _{0}}

λ =

linear,

σ =

surface charge density

🚫 Examiner Trap · Dipole & Gauss

(1) Axial field (

2 k p / r^{3}

) is

twice

the equatorial; both fall as

1/ r^{3}

, faster than a point charge. (2) A uniform field exerts

torque but no net force

on a dipole. (3) Gauss's

Φ

depends only on

enclosed

charge, but

E

on the surface depends on

all

charges. (4) Gauss is only

useful

for high symmetry (sphere/cylinder/sheet).

Electric Potential

Electric potential

V

: Work per unit positive charge to bring it from

\infty

to a point:

V = - \int_{\infty}^{r} E \cdot d r

. Scalar, unit volt (J

C^{- 1}

); only

differences

are physical.

Potential due to

V_{p o in t} = \frac{k q}{r}; V_{sys t e m} = \sum \frac{k q _{i}}{r _{i}}; V_{d i p o l e} = \frac{k p cos θ}{r ^{2}}

add V as a

scalar with sign

; dipole axial

k p / r^{2}

, equatorial

0

Field

\leftrightarrow

potential

E = - \frac{d V}{d r}; V_{B} - V_{A} = - \int_{A}^{B} E \cdot d r

E

points toward

decreasing

E =

-

(slope of V-r)

Concentric equipotential circles around a point charge, perpendicular to the radial field lines — Equipotentials $⊥$ field lines.

Equipotential surfaces

▸Always $⊥$ to field lines; $no work$ to move a charge along one.
▸Closer surfaces $\Rightarrow$ stronger field; a conductor (surface + interior) is one equipotential.
▸Two equipotentials never intersect.

🚫 Examiner Trap · Electric potential

(1) V is a

scalar

— add contributions with sign, not as vectors. (2)

E = 0

does

not

imply

V = 0

(e.g. inside a charged shell

E = 0

V \neq = 0

);

V = 0

does not imply

E = 0

(dipole equatorial). (3)

E = - d V / d r

: field points

down

the potential gradient. (4) Work by you

= q Δ V

; a

+

charge moves spontaneously from high to low V.

Potential Energy, Conductors & Dielectrics

Potential energy

U = \frac{k q _{1} q _{2}}{r}; U_{sys t e m} = pairs \sum \frac{k q _{i} q _{j}}{r _{ij}}

charge in external potential:

U = q V

; dipole in field:

U = - p \cdot E

Comparative: conductor vs dielectric

	Conductor	Dielectric
Free charges	yes	no (bound)
Field inside	$0$	$E_{0} / K$ (reduced)
Net charge sits	on surface	polarised, in bulk
In a capacitor	$K \to \infty$ effect	raises $C$ by $K$

A conductor in an external field develops induced surface charges so that the field inside is zero — Induced charges cancel the field inside.

Dielectrics

E_{in} = \frac{E _{0}}{K}; K = \frac{C}{C _{0}}; P = ε_{0} (K - 1) E

E_{0} =

applied field; polarisation

P

reduces the internal field;

D = ε_{0} E + P

🚫 Examiner Trap · PE, conductors & dielectrics

(1) Inside a conductor

E = 0

and

V =

const (even in a cavity — electrostatic shielding); charge lives on the

surface

. (2) A dielectric only

reduces

the field (

E_{0} / K

), never to zero (unlike a conductor). (3)

U_{sys t e m}

sums over

pairs

— don't double-count. (4) Polar molecules (

H_{2}

O) have permanent dipoles; non-polar (

N_{2}

) get induced ones.

Capacitance & Energy Stored

Capacitance

C

: Charge stored per unit potential difference

C = \frac{Q}{V}

. Unit farad (C

V^{- 1}

). Depends

only

on geometry and the medium, not on Q or V.

Parallel-plate

C = \frac{ε _{0} A}{d} dielectric C = \frac{K ε _{0} A}{d}

A =

plate area,

d =

separation,

K =

dielectric constant

Partial slab (thickness

t

)

C = \frac{ε _{0} A}{d - t + \frac{t}{K}}

conducting slab (

K \to \infty

C = \frac{ε _{0} A}{d - t}

Parallel-plate capacitor with +Q and -Q plates, a dielectric slab K between them and a uniform field — Dielectric raises $C$ by a factor $K$ .

Comparative: capacitor geometries

Type	$C$
Parallel-plate	$\frac{K ε _{0} A}{d}$
Spherical	$\frac{4 π ε _{0} ab}{b - a}$
Cylindrical	$\frac{2 π ε _{0} l}{ln ( b / a )}$
Isolated sphere	$4 π ε_{0} R$

Energy stored

U = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{Q ^{2}}{2 C}

energy density

u = \frac{1}{2} ε_{0} E^{2}

(in vacuum;

\frac{1}{2} K ε_{0} E^{2}

in a dielectric)

🚫 Examiner Trap · Capacitance & energy

(1) C depends on geometry/medium

only

— not on Q or V. (2) Pick the right energy form: with charge fixed use

Q^{2} /2 C

, with voltage fixed use

\frac{1}{2} C V^{2}

. (3) Inserting a dielectric with the

battery on

raises Q and energy; with the

battery off

lowers V and energy. (4) Force on a slab pulls it

in

(energy lowers).

Combination of Capacitors & RC Circuits

Comparative: series vs parallel

	Series	Parallel
Effective $C$	$\frac{1}{C} = \sum \frac{1}{C _{i}}$	$C = \sum C_{i}$
Same for all	charge $Q$	voltage $V$
Divides	$V \propto 1/ C$	$Q \propto C$
$C_{e ff}$ vs members	$<$ smallest	$>$ largest

Series / Parallel

\frac{1}{C _{s}} = \sum \frac{1}{C _{i}}; C_{p} = \sum C_{i}

series: same

Q

; parallel: same

V

Three capacitors in series and three in parallel with their effective-capacitance formulas — Series (same $Q$ ) vs parallel (same $V$ ).

RC charging / discharging

q = C V (1 - e^{- t / RC}); q = Q_{0} e^{- t / RC}

time constant

τ = RC

: reaches

63%

(charge) / falls to

37%

(discharge) in one

τ

Slab / battery rules

▸Battery $connected$ (V fixed): Q and energy change with C.
▸Battery $disconnected$ (Q fixed): V and energy change instead.

🚫 Examiner Trap · Combinations & RC

(1) Series C is

smaller

than the smallest member — opposite to resistors-in-series intuition. (2) Sharing charge between two capacitors

loses

energy (heat/radiation): common

V = \frac{C _{1} V _{1} + C _{2} V _{2}}{C _{1} + C _{2}}

. (3) At

t = 0

an uncharged capacitor acts as a

wire

(short); at

t = \infty

as a

break

(open). (4)

τ = RC

has units of seconds — check before using.

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What are the most important Electrostatics formulas for NEET?

This Electrostatics formula sheet covers all the high-yield Physics formulas, definitions and facts you need for NEET, across Electric charge, Coulomb’s law, electric field & field lines, Electric dipole, electric flux, Gauss’s law & applications, Electric potential & potential difference, equipotential surfaces, Conductors, dielectrics & polarisation, capacitors & combinations, Energy stored in a capacitor — each shown with the key result and, where useful, a worked example.

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How should I revise Electrostatics for NEET?

Blurt the Electrostatics key points from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

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