Table of Contents
Formula Flashcard — How to Use
Every formula for Electric Charges and Fields is below with its meaning, SI unit, notation, and exam note. Revise all 12 formulas in under 5 minutes. Bookmark for last-night board exam revision.
All Formulas
01
Quantization of Charge
Fundamental
$$q = \pm ne$$
where $e = 1.6 \times 10^{-19}$ C and $n = 1, 2, 3 \ldots$
Meaning
Charge exists only as integer multiples of the elementary charge. You cannot have half an electron’s charge as a free charge.
SI Unit
Coulomb (C)
📌 Board tip: Quarks carry fractional charge but are never found in isolation — so quantization still holds for any observable charge.
02
Coulomb’s Law
High Yield
$$F = \frac{1}{4\pi\varepsilon_0}\frac{|q_1 q_2|}{r^2} = k\frac{|q_1 q_2|}{r^2}$$
$k = 9 \times 10^9$ N m² C⁻² $\quad|\quad$ $\varepsilon_0 = 8.85 \times 10^{-12}$ C² N⁻¹ m⁻²
Meaning
Electrostatic force between two stationary point charges. Attractive for unlike charges, repulsive for like charges. Acts along the line joining them.
SI Unit
Newton (N)
$q_1, q_2$Point charges (C)
$r$Separation (m)
$k$Coulomb’s constant
$\varepsilon_0$Permittivity of free space
📌 In a medium: $F = \frac{kq_1q_2}{\varepsilon_r r^2}$ — divide by relative permittivity $\varepsilon_r$. Force decreases in a denser medium.
03
Electric Field Intensity
High Yield
$$\vec{E} = \frac{\vec{F}}{q_0} \qquad E = \frac{kq}{r^2}$$
Left: definition | Right: field due to a point charge $q$ at distance $r$
Meaning
Force per unit positive test charge. Direction: away from $+q$, towards $-q$. It is a vector — always mention direction in answers.
SI Unit
N C⁻¹ = V m⁻¹
📌 The test charge $q_0$ must be small enough not to disturb the source charge’s field.
04
Electric Dipole Moment
Definition
$$\vec{p} = q(2\vec{a})$$
Direction: from $-q$ to $+q$ (negative to positive)
Meaning
Measure of the strength of a dipole. $q$ is either charge, $2a$ is the separation between the two charges.
SI Unit
C·m
📌 Common trap: In chemistry, dipole direction is from $+$ to $-$. In physics it is the opposite — from $-$ to $+$.
05–06
Dipole Field — Axial & Equatorial
High Yield
Axial point (on dipole axis)
$$E_{axial} = \frac{2pr}{4\pi\varepsilon_0(r^2-a^2)^2}$$
Short dipole ($r \gg a$): $\displaystyle\frac{2p}{4\pi\varepsilon_0 r^3}$
Direction: along $\vec{p}$ →
Equatorial point (perpendicular bisector)
$$E_{eq} = \frac{p}{4\pi\varepsilon_0(r^2+a^2)^{3/2}}$$
Short dipole ($r \gg a$): $\displaystyle\frac{p}{4\pi\varepsilon_0 r^3}$
Direction: opposite to $\vec{p}$ ←
⭐ Key ratio (short dipole, same distance): $E_{axial} : E_{equatorial} = 2 : 1$ — asked almost every year in boards.
SI Unit
N C⁻¹
07
Torque on Dipole in Uniform Field
3–5 Marks
$$\vec{\tau} = \vec{p} \times \vec{E} \qquad \tau = pE\sin\theta$$
$\theta$ = angle between dipole moment $\vec{p}$ and field $\vec{E}$
Meaning
A dipole in a uniform field experiences a torque that tries to align it with the field. No net force in uniform field, but torque exists.
SI Unit
N·m
$\theta = 0°$$\tau = 0$, stable equilibrium
$\theta = 90°$$\tau = pE$ (maximum)
$\theta = 180°$$\tau = 0$, unstable equilibrium
08
Electric Flux
Definition
$$\Phi_E = \vec{E} \cdot \vec{A} = EA\cos\theta$$
Meaning
Total number of electric field lines passing through a surface. Maximum when field is perpendicular to surface ($\theta = 0°$). Zero when field is parallel to surface ($\theta = 90°$).
SI Unit
N m² C⁻¹
📌 Flux is a scalar. It can be positive, negative, or zero depending on the angle.
09
Gauss’s Law
High Yield
$$\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{q_{encl}}{\varepsilon_0}$$
Meaning
Total electric flux through any closed surface equals net enclosed charge ÷ $\varepsilon_0$. Flux depends only on charge inside — not on shape/size of surface or charges outside.
SI Unit
N m² C⁻¹
📌 Choose Gaussian surface where $\vec{E}$ is either parallel or perpendicular to $d\vec{A}$ everywhere — this simplifies the integral.
10–12
Gauss’s Law Applications
3 Derivations
10
Infinite Line Charge
Gaussian surface: cylinder
$$E = \frac{\lambda}{2\pi\varepsilon_0 r}$$
$\lambda$ = linear charge density (C m⁻¹) · $E \propto 1/r$ (not $1/r^2$)
11
Infinite Plane Sheet
Gaussian surface: pillbox (cylinder)
$$E = \frac{\sigma}{2\varepsilon_0}$$
$\sigma$ = surface charge density (C m⁻²) · $E$ independent of distance
12
Charged Spherical Shell
Gaussian surface: concentric sphere
$$E_{out} = \frac{kQ}{r^2},\quad E_{in} = 0$$
Outside ($r > R$): acts like point charge · Inside ($r < R$): field is zero
⭐ All three derivations asked in 3–5 mark questions every year. Know which Gaussian surface to use for each — this alone earns you half the marks.
Quick Reference — All Formulas at a Glance
| # | Formula Name | Formula | SI Unit |
|---|---|---|---|
| 1 | Charge Quantization | $q = \pm ne$ | C |
| 2 | Coulomb’s Law | $F = k|q_1q_2|/r^2$ | N |
| 3 | Electric Field | $E = kq/r^2$ | N C⁻¹ |
| 4 | Dipole Moment | $p = q(2a)$ | C·m |
| 5 | Axial Field (short dipole) | $E = 2p/4\pi\varepsilon_0 r^3$ | N C⁻¹ |
| 6 | Equatorial Field (short dipole) | $E = p/4\pi\varepsilon_0 r^3$ | N C⁻¹ |
| 7 | Torque on Dipole | $\tau = pE\sin\theta$ | N·m |
| 8 | Electric Flux | $\Phi = EA\cos\theta$ | N m² C⁻¹ |
| 9 | Gauss’s Law | $\Phi = q_{encl}/\varepsilon_0$ | N m² C⁻¹ |
| 10 | Line Charge Field | $E = \lambda/2\pi\varepsilon_0 r$ | N C⁻¹ |
| 11 | Plane Sheet Field | $E = \sigma/2\varepsilon_0$ | N C⁻¹ |
| 12 | Spherical Shell (outside) | $E = kQ/r^2$ | N C⁻¹ |
Key Constants
$e$$1.6 \times 10^{-19}$ CElementary charge
$k$$9 \times 10^{9}$ N m² C⁻²Coulomb’s constant
$\varepsilon_0$$8.85 \times 10^{-12}$ C² N⁻¹ m⁻²Permittivity of free space
$m_e$$9.1 \times 10^{-31}$ kgMass of electron
Board Exam Tips
Tip 1 — Three Gauss’s Law derivations (3–5 marks each)
Memorise the Gaussian surface for each: cylinder for line charge, pillbox for plane sheet, concentric sphere for spherical shell. The surface choice alone fetches you marks even if you lose a step.
Tip 2 — $E_{axial} : E_{equatorial} = 2:1$ (1 mark)
This ratio for a short dipole at the same distance appears almost every year as a 1-mark question. Write it down as a fact: axial field is twice the equatorial field.
Don’t confuse — $\sigma/2\varepsilon_0$ vs $\sigma/\varepsilon_0$
Single infinite sheet: $E = \sigma/2\varepsilon_0$ · Between two oppositely charged parallel plates (capacitor): $E = \sigma/\varepsilon_0$. The factor of 2 is the most common error in this chapter.
Remember — Superposition Principle
When multiple charges are present, the net electric field or force at a point is the vector sum of individual contributions. Always resolve into components before adding.
