In this chapter, you will learn
- —Understand magnetic field around current-carrying conductor
- —Learn Ampere's circuital law and calculate field strength
- —Study solenoids and electromagnets
- —Learn force on current-carrying conductor in magnetic field
- —Understand motor principle and DC motor construction
- —Learn electromagnetic induction and Faraday's law
- —Understand Lenz's law and energy conservation
- —Study AC generators and transformer principles
Magnetic Field Around Current-Carrying Wire
A current-carrying conductor creates a magnetic field around it. The field pattern is concentric circles perpendicular to the wire.
Ampere's Circuital Law:
B = μ₀I / (2πr)
where B = magnetic field strength, μ₀ = permeability (4π × 10⁻⁷), I = current, r = distance from wire
Right-Hand Rule:
- Point thumb in direction of current
- Fingers curl in direction of magnetic field lines
- Field lines form concentric circles around wire
- Closer to wire: Stronger field (inversely proportional to r)
- Farther from wire: Weaker field
Key Points:
- Magnetic field strength B inversely proportional to distance (B ∝ 1/r)
- Magnetic field directly proportional to current (B ∝ I)
- Field is perpendicular to current direction
- No field along wire axis, only perpendicular to it
- Field can be detected using compass needle or iron filings
Exam Tip
Remember right-hand rule: Thumb = current direction, Fingers = field direction. B ∝ I/r formula is crucial.
Common Mistake
Students forget right-hand rule direction. Practice it repeatedly - thumb with current, fingers show field direction.
Solenoid and Magnetic Field
A solenoid is a coil of wire wound tightly on a cylinder. It creates uniform magnetic field inside, similar to a bar magnet.
Solenoid Characteristics:
- Inside solenoid: Strong, uniform magnetic field parallel to axis. Field strength B = μ₀nI
- Outside solenoid: Field very weak (nearly zero). Field lines confined inside
- n = number of turns per unit length. More turns = stronger field (B ∝ n)
- Field strength directly proportional to current: Higher current = stronger field (B ∝ I)
- Field pattern: Inside uniform, Outside negligible. Unlike bar magnet.
- North and South poles: Determined by right-hand rule applied to solenoid
Magnetic Field in Solenoid:
B = μ₀nI
where n = turns per unit length, I = current
Applications of Solenoids:
- Electromagnets (with soft iron core): Temporary strong magnets
- Electric bells: Solenoid attracts hammer mechanism
- Relays: Solenoid controls switch
- Door locks: Solenoid pushes/pulls latch
- Starter motors: Solenoid engages engine flywheel
Exam Tip
B = μ₀nI for solenoid. Inside uniform field, outside negligible. More turns and more current = stronger field.
Common Mistake
Students think solenoid has same field outside as bar magnet. WRONG! Solenoid field is mostly confined inside.
Electromagnet and Force on Conductor
An electromagnet is a solenoid with soft iron core that becomes magnetic when current flows. Force on current-carrying conductor in magnetic field given by F = BIL sinθ.
Force on Current-Carrying Conductor:
F = BIL sinθ
where B = magnetic field, I = current, L = length of conductor, θ = angle between current and field
Electromagnet Properties:
- Soft iron core: Magnetizes when current flows, demagnetizes when current stops (temporary magnet)
- Strength controllable: Change current (higher I = stronger) or number of turns (more n = stronger)
- Polarity reversible: Reverse current direction to reverse poles
- vs Permanent magnet: Electromagnet controllable, permanent magnet not
- Applications: Electric bells, door locks, cranes lifting scrap metal, MRI machines
Direction of Force (Fleming's Left-Hand Rule):
- Left hand: Thumb = force direction, Index = field direction (N to S), Middle = current direction
- Maximum force when θ = 90° (conductor perpendicular to field): F = BIL
- Zero force when θ = 0° (conductor parallel to field)
- Reversing current reverses force direction
- Reversing field reverses force direction
Exam Tip
F = BIL sinθ. Maximum force when perpendicular (θ=90°). Fleming's left-hand rule for force direction.
Common Mistake
Students confuse Fleming's left (force/motor) with right (generator) hand rule. LEFT for motor, RIGHT for generator.
DC Motor and Motor Principle
A DC motor converts electrical energy to mechanical energy using magnetic force on current-carrying coil. Based on motor principle: force on current-carrying conductor in magnetic field causes rotation.
DC Motor Components:
- Coil (armature): Carries current, rotates in magnetic field
- Magnetic field: Permanent magnet or electromagnet creating field
- Split-ring commutator: Two half-rings electrically connected to coil. Reverses current direction every half rotation
- Brushes: Carbon contacts sliding on commutator, deliver current to coil
- Axle: Rotates with coil, does mechanical work
- Shaft/bearings: Support and allow rotation
Motor Principle:
Current in magnetic field experiences force (F = BIL). Force on opposite sides of coil in opposite directions causes rotation.
How Split-Ring Commutator Works:
- Current enters coil through brush touching commutator half-ring A
- Exits through brush touching commutator half-ring B
- Coil experiences force: Side 1 pushed up, Side 2 pushed down (or vice versa) = rotation
- After half rotation: Commutator halves switch brushes
- Current direction in coil reverses, keeping forces in same rotational direction
- Continuous rotation as long as current flows
- Without commutator: Coil would oscillate back-and-forth, not rotate continuously
Speed and Torque Control:
- Increase current: Stronger force → higher speed and torque
- Increase magnetic field: Stronger force → higher speed and torque
- Increase coil turns: Greater effective conductor length → higher torque
- Increase coil area: More conductor in field → higher torque
Exam Tip
DC motor uses split-ring commutator to reverse current direction, keeping rotation continuous. Draw motor diagram with coil, field, and commutator.
Common Mistake
Students think commutator just conducts current. WRONG! Commutator reverses current direction every half rotation to sustain rotation.
Electromagnetic Induction and Faraday's Law
Electromagnetic induction is generation of electric current (or EMF) by changing magnetic flux through a conductor. This is the reverse of motor effect.
Faraday's Law of Electromagnetic Induction:
ε = -N(dΦ/dt)
where ε = induced EMF, N = number of turns, dΦ/dt = rate of change of magnetic flux
Ways to Induce EMF:
- Change magnetic flux: Move conductor in magnetic field, rotate coil in field, or vary field strength
- Key: Rate of change of flux. Faster change → larger EMF
- Magnetic flux Φ = BA cosθ: B = field strength, A = area, θ = angle between field and normal
- Zero EMF when: Flux not changing (stationary coil in uniform field)
- Maximum EMF when: Coil perpendicular to field (fastest flux change rate)
Lenz's Law:
- Direction of induced current: Always opposes the change causing it
- Induced field opposes change: If external flux increasing, induced field opposes (decreases)
- Consequence: Always requires work to move conductor/change field → energy conservation
- Sign in Faraday's law: Negative sign indicates opposition (Lenz's law)
Applications:
- Electric generators: Mechanical rotation → electrical energy
- Transformers: Changing AC magnetic field induces current in secondary coil
- Induction cooktop: Changing current in coil creates changing field, inducing current in pot
- Metal detectors: Changing field in detector coil detects metal
Exam Tip
Faraday's law ε = -N(dΦ/dt). Lenz's law: induced current opposes change. Faster flux change = larger EMF.
Common Mistake
Students ignore the negative sign in Faraday's law. It represents Lenz's law (opposition to change).
AC Generator and Transformer
An AC generator rotates a coil in magnetic field to produce alternating current. A transformer uses changing magnetic field to transfer electrical power between coils with different voltage.
AC Generator (Alternator):
- Coil rotates in magnetic field. As it rotates, flux through coil changes sinusoidally
- Induced EMF: ε = ε₀ sin(ωt) - sinusoidal with time
- ε₀ = NABω: Maximum EMF depends on turns, area, field, and angular velocity
- Slip rings: Allow rotating coil to deliver current to external circuit
- Output: Alternating current (AC) - voltage and current reverse direction periodically
- Frequency: 50 Hz (India, Europe) or 60 Hz (USA) - number of complete cycles per second
Transformer Principle:
Vs/Vp = Ns/Np
where Vs = secondary voltage, Vp = primary voltage, Ns = secondary turns, Np = primary turns
Transformer:
- Step-up transformer: Ns > Np → Vs > Vp (higher voltage, lower current)
- Step-down transformer: Ns < Np → Vs < Vp (lower voltage, higher current)
- Power conservation (ideal): Pp = Ps → Vp × Ip = Vs × Is
- Current relationship: Is/Ip = Np/Ns (inverse of voltage ratio)
- Core: Iron core increases magnetic coupling between coils, increases efficiency
- AC only: Transformer requires changing flux - DC won't work!
- Application: Power transmission (step up voltage to reduce losses), home appliances (step down)
Exam Tip
Transformer: Vs/Vp = Ns/Np. Step-up increases V, step-down decreases V. Works only with AC (changing flux).
Common Mistake
Students think transformer works with DC. WRONG! Transformer requires changing flux from AC. DC produces constant field.