Ch 09: Electrostatics | Exam Fusion Prep

⚡ Chapter At a Glance

9×10⁹

Coulomb's Constant K (Nm²/C²)

1.6×10⁻¹⁹C

Magnitude of Electron Charge

Farad

Unit of Capacitance

Silver

Best Conductor

Electrostatics — branch of physics dealing with electric charges at rest
Key laws: Coulomb's Law · Ohm's Law · Faraday's Law of Electrolysis
Key concepts: Charge properties · Electric field · Potential · Capacitance · Resistance · Cells
Key instruments: Ammeter (series) · Voltmeter (parallel) · Galvanometer

📋 Key Formulae — Quick Look

F = K(q₁q₂)/r²Coulomb's Law

V = W/q₀Electric Potential

C = Q/VCapacitance

V = IR | P = VI = I²ROhm's Law & Power

R = ρl/AResistance Formula

H = I²RtJoule's Heating Effect

⚡ Electric Charge — Properties

📘 Definition

Basic property of matter due to which it produces and experiences electrical and magnetic effects. Unit: Coulomb (C).

Property I

Additive Nature

Q = q₁ + q₂ + q₃Total charge = algebraic sum of all charges

Property II

Quantisation

Charge exists in integral multiples of the electronic charge.

Q = ne | e = 1.602176634 × 10⁻¹⁹ C (positive magnitude; n is a signed integer)n = integer, e = electronic charge

Property III

Conservation

Charge can neither be created nor destroyed. Total charge of an isolated system remains constant.

Property IV

Attraction & Repulsion

Same charges → Repulsion
Opposite charges → Attraction

🔗 Coulomb's Law

F = K(q₁q₂)/r²Force between two point charges

K (Coulomb's constant)

9 × 10⁹ Nm²/C²

K = 1/4πε₀

ε₀ = 8.85×10⁻¹² C²/Nm²

ε₀

Permittivity of Vacuum

⚠️ Exam Trap — Coulomb's Law

Force ∝ product of charges & inversely ∝ square of distance (inverse square law)
K = 9 × 10⁹ Nm²/C² — must memorize
Coulomb's law is valid for point charges only
Similar to Newton's gravitation law but can be repulsive too

🧱 Classification of Materials by Conductivity

✅ Conductor

Charge flows easily
Has free electrons
Silver (best), Gold, Copper, Graphite, Sea water

🚫 Insulator

Charge does NOT flow
No free electrons
Rubber, oil, polythene, very pure water; lead is a metal conductor

⚙️ Semiconductor

Between conductor & insulator
Conductivity varies with conditions
Silicon, Germanium

⚠️ Exam Trap

Silver is the best conductor (NOT copper or gold)
Pure water is an insulator; sea water is a conductor (dissolved salts = ions)
Silicon and germanium are common semiconductor examples

🌐 Electric Field & Intensity

📘 Electric Field

The space surrounding an electric charge in which any other charge experiences a force of attraction or repulsion.

📘 Intensity of Electric Field (E)

Ratio of force applied on a test charge at a point to the magnitude of the test charge.

Unit

N/C

Quantity

Vector

📏 Electric Field Lines — Properties

Direction: Positive → Negative charge
Non-intersecting — two field lines never cross
Do NOT form closed loops
Electrostatic field is conservative
Closer lines = stronger field; farther lines = weaker field
Perpendicular to a conductor’s surface in electrostatic equilibrium

⚠️ Exam Trap — Field Lines

Electric field lines never intersect each other. If they did, there would be two directions of force at that point — impossible. Field lines go FROM + TO − charge.

🔋 Electric Potential & Potential Difference

Electric Potential (V)

Work done to bring unit +ve charge from ∞ to a point

V = W/q₀Unit: Volt (V) or J/C | Scalar

Potential Difference (V_A − V_B)

Work done to move unit +ve charge between two points

Va − Vb = W/q₀Unit: Volt | Scalar

📘 Solved Example

Work = 2.25 J, Charge = 12 × 10⁻⁴ C
V = W/q = 2.25 / (12 × 10⁻⁴) = 1875 Volt

🔲 Capacitance & Capacitor

📘 Capacitor

A capacitor stores separated charge and electrostatic energy, generally on two conductors separated by an insulating region

C = Q/VCapacitance | Unit: Farad (F) = Coulomb/Volt

📘 Solved Example

C = 1.0 μF = 1.0 × 10⁻⁶ F, V = 6.0 kV = 6.0 × 10³ V
Q = CV = 1.0×10⁻⁶ × 6.0×10³ = 6 × 10⁻³ Coulomb

⚠️ Exam Trap

Capacitance unit = Farad (not Ohm, not Volt). 1 Farad = 1 Coulomb/Volt. Practical units: μF (microfarad) and pF (picofarad).

🔋 Electric Current

i = q/tElectric Current | Unit: Ampere (A) = C/s

Ampere

SI Unit of Current

6.25×10¹⁸

Electrons per second (1A)

Property	Details
Direction of current	Opposite to direction of electron flow (conventional)
Flow direction	Through a passive resistor/external load: high → low potential
In solids	By free electrons
In liquids	In electrolytes, current is carried by positive and negative ions
In semiconductors	By holes and electrons

AC — Alternating Current

Direction alternates periodically

Used in: Household supply, generators, transformers

DC — Direct Current

Direction remains constant

Used in: Batteries, electronic circuits, charging

📐 Ohm's Law

📘 Statement

If physical conditions (temperature etc.) of a conductor remain unchanged, the potential difference across it is proportional to the current through it.

V ∝ I → V = IROhm's Law | Proposed by George Simon Ohm (1827)

Proposed by

George Simon Ohm

Year

1827

R = constant =

Resistance

Ohmic Resistance

Obeys Ohm's Law

V-I graph is a straight line.
Example: Manganin wire at constant temperature

Non-Ohmic Resistance

Does NOT obey Ohm's Law

V-I graph is non-linear.
Example: Diode, bulb

⚠️ Exam Trap — Ohm's Law

Ohm's Law is valid only when temperature & physical conditions are constant
Through a passive resistor/external load, conventional current flows from high to low potential
Electrons flow from low to high potential (opposite to conventional current)

🔩 Electric Resistance

📘 Definition

Property of a conductor that opposes the flow of electric current.

Unit

Ohm (Ω)

R ∝ Length

More length → More R

R ∝ 1/Area

More area → Less R

R = ρl/Aρ (rho) = Specific Resistance (Resistivity)

🔀 Series vs Parallel Combination

➡️ Series Combination

R_eq = R₁ + R₂ + R₃Equivalent resistance

Current is equal through all
Voltage drops depend on resistance; equal resistors have equal drops
R_eq is always greater than any individual R
Uses: Fuse, Ammeter

⇉ Parallel Combination

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃Equivalent resistance

Branch currents depend on resistance; equal branches carry equal currents
Potential difference is equal
R_eq is always less than smallest R
Uses: Domestic wiring, Voltmeter

⚠️ Exam Trap — Series vs Parallel

Series: same current; voltage drops depend on resistance
Parallel: same voltage; branch currents depend on resistance
Household wiring = parallel (each appliance gets full voltage)
Ammeter connected in series; Voltmeter in parallel

📊 Resistivity & Conductance

Resistivity (ρ)

Specific Resistance

ρ = RA/lUnit: Ω·m

Conductance (G)

Inverse of Resistance

G = 1/RUnit: Siemens (S) or Ω⁻¹

Specific Conductivity (σ)

Inverse of Resistivity

σ = 1/ρUnit: Ω⁻¹m⁻¹

Material	Resistivity (Ω·m)
Silver	1.60 × 10⁻⁸
Copper	~1.7 × 10⁻⁸
Aluminium	~2.7 × 10⁻⁸
Tungsten	~5.6 × 10⁻⁸
Nickel	~7 × 10⁻⁸
Iron	10 × 10⁻⁸
Constantan	4.9 × 10⁻⁷
Manganin	4.4 × 10⁻⁷
Nichrome	1.0 × 10⁻⁶
Glass	10¹⁰–10¹⁴
Rubber	10¹³–10¹⁶

📘 Solved Example

Wire: l = 15 m, A = 6×10⁻⁷ m², R = 5 Ω
ρ = RA/l = 5 × 6×10⁻⁷ / 15 = 2×10⁻⁷ Ω·m

🔥 Heating Effect of Electric Current

📘 Joule's Law

When electric current flows through a conductor, heat energy is produced due to resistance.

H = I²Rt Joules = I²Rt/4.2 caloriesJoule's Law of Heating

W = VIt = I²Rt = V²t/RElectrical Energy / Work Done

P = VI = V²/R = I²RElectric Power | Unit: Watt (W), Horsepower (HP)

Energy Unit

Joule or kWh

Power Unit

Watt or HP

1 kWh =

1 Unit of Electricity

🏠 Applications of Heating Effect

Appliance	Key Details
Electric Bulb	Filament: Thin Tungsten wire \| High resistivity, Melting point 3422°C \| Protective fill gas: N₂ + Argon \| Operating temp: 1500–2500°C
Electric Press (Iron)	Wire: Nichrome (80% Nickel + 20% Chromium)
Electric Heater	Ceramic plate + Nichrome wire
Fuse	Protects against short circuit & overloading \| Fuse wire material depends on design; low-melting alloys are common \| Modern: MCB (Miniature Circuit Breaker)

⚠️ Exam Trap — Heating Applications

Bulb filament = Tungsten (highest melting point among metals, approximately 3422°C)
Heater/Iron wire = Nichrome (Ni + Cr)
Fuse = low melting point alloy (material varies by fuse design) — melts to break circuit
MCB = modern replacement of fuse — can be reset unlike fuse
Protective gas in bulb = Nitrogen + Argon (prevents tungsten oxidation)

⚗️ Chemical Effect of Electric Current

Electrolysis is chemical change at electrodes caused by current through an electrolyte; ion dissociation alone is not electrolysis
Law of Electrolysis proposed by: Faraday
Applications: Electric cell, Electroplating

🔌 Electric Cell

📘 Definition

Converts chemical energy → electrical energy.

EMF: E = W/q (Volt) | Terminal PD: V = E − irEMF and Terminal Potential Difference

Current: I = E/(R+r) | Internal resistance: r = (E/V − 1)RCell current and internal resistance

Primary Cell

Chemical → Electrical (one-time use)

Cannot be recharged. Chemical energy directly converted to electrical.

Secondary Cell

Rechargeable

Electrical → Chemical (charging), then Chemical → Electrical (discharging). Can be reused.

📊 Types of Cells — Details

Type	Cell Name	Anode	Cathode	EMF (V)	Int. Resistance
Primary	Voltaic cell	Zinc	Copper	Variable; not a voltage standard	Depends on design, state and conditions
Primary	Leclanché cell	Zinc	MnO₂ mixture; carbon collector	~1.5 V nominal	Depends on design, state and conditions
Primary	Zinc–carbon dry cell	Zinc	MnO₂–carbon mixture	~1.5 V nominal	Depends on design, state and conditions
Primary	Daniell cell	Zinc	Copper	~1.10 V	Depends on design, state and conditions
Primary	Bichromate cell	Zinc	Carbon	~2 V; construction-dependent	Depends on design, state and conditions
Standard reference (non-rechargeable)	Weston cadmium cell	Cadmium amalgam	Mercury/mercurous sulfate	~1.0186 V near 20°C	Depends on design, state and conditions
Secondary	Lead–acid accumulator (discharging)	Spongy Pb (negative)	PbO₂ (positive)	~2.0 V nominal per cell	Depends on design, state and conditions
Primary	Alkaline Zn–MnO₂ cell	Zinc	MnO₂	~1.5 V nominal	Depends on design, state and conditions

⚠️ Exam Trap — Cells

Dry cell / Leclanche: both Zinc-Carbon, EMF = approximately 1.5 V nominal
Lead Accumulator (car battery): PbO₂ cathode, EMF = approximately 2.0 V nominal per cell
Secondary cells are rechargeable; Primary cells are not
Lower internal resistance reduces voltage loss under load; cell suitability also depends on chemistry, capacity and intended use

🧰 Electrical Measuring Instruments

Instrument	Measures	Connection	Ideal Resistance	Symbol
Ammeter	Electric Current	Series	Zero (0)	(+)—(A)—(−)
Voltmeter	Potential Difference	Parallel	Infinite (∞)	(+)—(V)—(−)
Galvanometer	Detects current (direction & magnitude)	—	Medium	—(G)—

Galvanometer Conversions

Converting Galvanometer into Other Instruments

Galvanometer + Low resistance in parallel → Ammeter
Galvanometer + High resistance in series → Voltmeter

⚠️ Exam Trap — Instruments

Ammeter in series (low resistance — must not disturb current)
Voltmeter in parallel (high resistance — must not draw current)
Ideal Ammeter resistance = 0; Ideal Voltmeter resistance = ∞
Galvanometer → Ammeter: add shunt (low R in parallel)
Galvanometer → Voltmeter: add high R in series

🎯 High-Yield Exam Points

Charge unit: coulomb. Electron charge = −1.602176634 × 10⁻¹⁹ C; e denotes the positive magnitude
Properties of charge: Additive, Quantised (Q=ne), Conserved, Attraction/Repulsion
Coulomb's Law: F = Kq₁q₂/r² | K = 9 × 10⁹ Nm²/C²
Silver = best conductor; Silicon & Germanium = semiconductors
Electric field lines: + to −, non-intersecting, no closed loops
Electric Potential: Scalar, unit = Volt = J/C
Capacitance unit = Farad | C = Q/V
Current unit = Ampere | i = q/t | 1A = 6.25 × 10¹⁸ e/s
Current direction = opposite to electron flow
Ohm's Law (1827): V = IR; valid at constant temperature
Series: same current, R adds; Parallel: same voltage, 1/R adds
Domestic wiring = parallel
Resistivity ρ = RA/l | Unit = Ω·m
Joule's heating: H = I²Rt; Power P = VI = I²R = V²/R
Bulb filament = Tungsten; Heater/Iron = Nichrome
Fuse = low-melting fuse element (composition varies); modern = MCB
Electrolysis law by Faraday
Lead accumulator EMF = approximately 2.0 V nominal per cell; Dry cell EMF = approximately 1.5 V nominal
Ammeter: series, R=0; Voltmeter: parallel, R=∞
Galvanometer → Ammeter: low R parallel; → Voltmeter: high R series

📋 Formula Quick Reference

Q = ne | e = 1.6×10⁻¹⁹CQuantisation of charge

F = K·q₁q₂/r²Coulomb's Law | K=9×10⁹

C = Q/VCapacitance (Farad)

V = IR | P = VI = I²ROhm's Law & Power

R = ρl/AResistance

H = I²RtJoule's Heating

I = E/(R+r)Cell Current

⚠️ Most Common Exam Traps

Best conductor = Silver (NOT copper)
Pure water = insulator; Sea water = conductor
Current flows opposite to electron movement
Ammeter → series, zero resistance; Voltmeter → parallel, infinite resistance
Domestic wiring = parallel (not series)
Bulb = Tungsten; Heater = Nichrome (not swapped)
Fuse melts (breaks) on excess current; MCB trips and can be reset
Ohm's Law: only valid at constant physical conditions
Electrolysis = Faraday's law
EMF unit = Volt (same as potential, not Ampere)

⚡ Chapter 09: Electrostatics