Topic 10
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Topic 10 — Key Facts for DU Admission (Bangladesh) Core concept: Electricity and Magnetism — fundamental laws and applications High-yield point: Ohm’s Law, Kirchhoff’s Laws, magnetic effects of current ⚡ Exam tip: Numerical problems from Ohm’s Law, resistance combinations, and electromagnetic induction appear frequently
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Standard content for students with a few days to months.
Topic 10 — DU Admission (Bangladesh) Study Guide Overview: Electricity and Magnetism covers electric circuits, magnetic fields, and electromagnetic induction Core principles: Ohm’s Law, Kirchhoff’s Laws, Faraday’s Laws, Lorentz force Key points: Series/parallel circuits, magnetic field around conductor, AC/DC generators Study strategy: Master circuit analysis with diagrams, memorize all formulas
🔴 Extended — Deep Study (3mo+)
Comprehensive coverage for students on a longer study timeline.
Electricity and Magnetism — Complete Study Notes
Part A: Electricity
Electric Charge
- Positive charge: Due to loss of electrons (cation)
- Negative charge: Due to gain of electrons (anion)
- Charge on electron: e = −1.6 × 10⁻¹⁹ C
- Quantization: Q = ne (where n = integer)
- Law of charges: Like charges repel, unlike charges attract
- Conservation: Charge can neither be created nor destroyed
Electric Current
- Current (I): Rate of flow of charge
- I = Q/t (Ampere = Coulomb/second)
- Direction: Conventionally from + to − (opposite to electron flow)
- Electron flow: Actual direction ( − to +)
- Charge carrier: Electron in metals, ion in electrolytes
Potential and Potential Difference
- Electric potential (V): Work done to bring unit positive charge from infinity to point
- Potential difference: V = W/Q = J/C = Volt
- 1 Volt: Potential difference when 1 joule work is done moving 1 coulomb charge
Ohm’s Law
V = IR
Where:
- V = Potential difference (Volt)
- I = Current (Ampere)
- R = Resistance (Ohm, Ω)
Limitations:
- Does not apply to non-ohmic conductors (diode, transistor)
- Does not apply when temperature changes significantly
Resistance
R = ρL/A
Where:
- ρ = Resistivity (Ω·m) — material property
- L = Length (m)
- A = Cross-sectional area (m²)
Factors affecting resistance:
- R ∝ L (directly proportional to length)
- R ∝ 1/A (inversely proportional to area)
- R ∝ ρ (depends on material)
- R increases with temperature (for metals)
Superconductors: Zero resistance below critical temperature (e.g., Mercury below 4.2 K)
Resistors in Series
- Same current through all resistors
- Total voltage: V = V₁ + V₂ + V₃
- Total resistance: R = R₁ + R₂ + R₃
- Voltage division: V₁/V₂ = R₁/R₂
Resistors in Parallel
- Same voltage across all resistors
- Total current: I = I₁ + I₂ + I₃
- 1/R = 1/R₁ + 1/R₂ + 1/R₃
- Current division: I₁/I₂ = R₂/R₁
Electric Power
P = VI = I²R = V²/R
- SI unit: Watt (W)
- 1 horsepower = 746 W
- Energy consumed: W = Pt = VIt
Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL)
At any junction, sum of currents entering = sum of currents leaving
- Based on conservation of charge
Kirchhoff’s Voltage Law (KVL)
In any closed loop, sum of EMFs = sum of potential drops
- Based on conservation of energy
Cells and EMFs
- EMF (ε): Potential difference across cell terminals when no current flows
- Terminal voltage (V): P.D. when current flows through external resistance
- V = ε − Ir (where r = internal resistance)
- Internal resistance: Resistance offered by electrolyte inside cell
- For maximum current: External resistance = Internal resistance (R = r)
Combination of Cells
| Combination | Condition | Total EMF | Total Internal Resistance |
|---|---|---|---|
| Series | Same direction | nε | nr |
| Parallel | Identical cells | ε | r/n |
Heating Effect of Current
Joule’s Law of Heating: H = I²Rt = V²t/R = VIt
- All electrical energy eventually converts to heat
- Filament of bulb: Tungsten (high melting point 3380°C)
- Fuse wire: Lead-tin alloy (low melting point)
Chemical Effect of Current
- Electrolyte: Solution that conducts electricity with chemical change
- Electrolytes: Acids, bases, salts in solution
- Non-electrolytes: Sugar, alcohol (no ions)
- Electrolytic dissociation: Separation of ions in solution
- Faraday’s Laws of Electrolysis:
- m = ZIt (mass deposited)
- Z = electrochemical equivalent
Part B: Magnetism
Magnetic Field
- Region around magnet where force can be detected
- Magnetic field lines: Emerge from N-pole, enter S-pole (outside magnet)
- Inside magnet: S to N (closed loops)
- Magnetic flux (φ): Total magnetic field passing through area (Weber, Wb)
- Magnetic flux density (B): Flux per unit area (Tesla, T)
Earth’s Magnetic Field
- Earth behaves as a huge magnet
- Magnetic north ≈ Geographic south (and vice versa)
- Magnetic declination: Angle between geographic and magnetic meridian
- Magnetic inclination/dip: Angle magnetic needle makes with horizontal
Magnetic Effects of Current
Oersted’s Experiment (1820)
Current through straight conductor produces circular magnetic field around it.
- Right-hand thumb rule: Thumb = current direction, fingers = field direction
Magnetic Field Formulas
Near straight conductor: B = (μ₀/4π) × (2I/d)
Near circular coil (at center): B = (μ₀/4π) × (2πnI/r) = μ₀nI/2r
Near solenoid: B = μ₀nI (inside solenoid, uniform field) Where n = N/L (turns per unit length)
Ampere’s Swimming Rule
If a man swims along a conductor with current, facing the compass needle — current from left to right, north pole deflects towards his left hand side.
Force on Current-Carrying Conductor in Magnetic Field
F = BIL sinθ
Where:
- B = Magnetic field strength
- I = Current
- L = Length of conductor
- θ = Angle between conductor and field
Fleming’s Left-Hand Rule:
- Thumb = Force
- First finger = Magnetic field (N to S)
- Second finger = Current (positive to negative)
Force on Moving Charge in Magnetic Field
F = qvB sinθ
- Perpendicular to both v and B
- No force when charge moves parallel to field
- Maximum force when charge moves perpendicular to field
- q = 0 for neutron (no magnetic effect)
Circular Motion in Magnetic Field
When a charged particle enters perpendicular to magnetic field:
- Radius: r = mv/qB
- Time period: T = 2πm/qB (independent of velocity)
- Important: Cyclotron uses this principle
Electromagnetic Induction
Faraday’s Experiments:
- Moving magnet near coil → current induced
- Moving coil near stationary magnet → current induced
- Changing current in one coil → current induced in nearby coil
Faraday’s Laws of Electromagnetic Induction
First Law: Whenever magnetic flux linked with a coil changes, an EMF is induced. Second Law: Induced EMF is directly proportional to rate of change of flux.
ε = −N dφ/dt
The negative sign indicates Lenz’s Law.
Lenz’s Law
Induced current flows in such a direction that it opposes the change in magnetic flux that produced it.
- Conservation of energy → Lenz’s Law is a consequence of energy conservation
Motional EMF
When a conductor moves in magnetic field: ε = Bvl (perpendicular to field)
- Used in DC generator, ** Moving coil microphone**
Self-Induction and Mutual Induction
Self-induction:
- Coil opposes change in its own current
- ε = −L dI/dt
- L = Self-inductance (Henry, H)
Mutual induction:
- Change in current in one coil induces EMF in nearby coil
- ε₂ = −M dI₁/dt
- M = Mutual inductance
AC and DC
| Feature | AC (Alternating Current) | DC (Direct Current) |
|---|---|---|
| Direction | Reverses periodically | Constant |
| Frequency | 50 Hz (BD/India) | 0 Hz |
| Transmission | Easy (transformer) | Difficult |
| Generation | AC Generator | DC Generator/Battery |
AC Generator (Dynamo)
- Converts mechanical energy → electrical energy
- ε = ε₀ sin ωt where ε₀ = NBAω (peak EMF)
- Slip rings → AC output
- Commutator → DC output
Transformer
Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ
- Step-up: Vₛ > Vₚ (Nₛ > Nₚ)
- Step-down: Vₛ < Vₚ (Nₛ < Nₚ)
- Efficiency = (V₂I₂)/(V₁I₁) × 100%
- Ideal transformer: 100% efficient (no energy loss)
Must-Remember Formulas
| Formula | Application |
|---|---|
| V = IR | Ohm’s Law |
| R = ρL/A | Resistance calculation |
| P = VI = I²R | Electric power |
| F = BIL sinθ | Force on conductor |
| F = qvB sinθ | Force on moving charge |
| r = mv/qB | Radius of circular path |
| ε = −N dφ/dt | Faraday’s Law |
| ε = Bvl | Motional EMF |
| Vₛ/Vₚ = Nₛ/Nₚ | Transformer ratio |
Must-Remember Facts
- Right-hand thumb rule: Current direction vs field direction
- Fleming’s left-hand rule: Force on current-carrying conductor
- Fleming’s right-hand rule: Direction of induced current (generator)
- Lenz’s Law: Induced EMF opposes change in flux (energy conservation)
- Transformer works only for AC (not DC)
- Cyclotron frequency T = 2πm/qB (independent of velocity)
- 1 Tesla = 10,000 Gauss
- μ₀ (permeability of free space) = 4π × 10⁻⁷ H/m
- Efficiency of transformer increases with core lamination
Common DU Admission Questions
- Series and parallel resistance calculation
- Ohm’s Law numerical problems
- Force on current-carrying conductor in magnetic field
- Faraday’s law of electromagnetic induction
- Transformer ratio (step-up/step-down)
- KCL and KVL application in circuits
- Oersted’s experiment and magnetic field around conductor
Exam Tips
- In series circuit: Current same, voltage divides proportionally
- In parallel circuit: Voltage same, current divides inversely
- When solving circuits with Kirchhoff’s Laws: Write as many independent equations as unknown currents
- Lenz’s Law always opposes the cause — always check direction of induced current
- For electromagnetic induction: Remember “Rate of change of flux” — not flux itself
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