A magnetic field is the region around a magnet or current-carrying conductor where magnetic forces can be detected. It is represented by field lines: they emerge from the north pole and enter the south pole; the density of lines indicates field strength.
Magnetic Field
Electromagnetism
Induction
Applications
NCERT Class 10 — Magnetic Effects of Electric Current
Hans Christian Oersted observed that a compass needle deflects when placed near a current-carrying wire, proving current produces a magnetic field. This discovery linked electricity and magnetism foundational to electromagnetism.
If you hold a straight conductor with your right thumb pointing in the direction of conventional current, the fingers show the direction of the magnetic field lines (concentric circles around the wire).
Magnitude at distance r from a long straight wire: B = μ₀ I / (2π r) (in free space), where μ₀ is permeability of free space.
A circular loop produces a field similar to a bar magnet: field lines pass through the centre and emerge from one face to the other. For a coil (solenoid) the field inside is strong and uniform, outside resembles that of a bar magnet. Use right-hand curl rule: curl fingers along current, thumb gives north pole direction.
For an ideal long solenoid: B = μ₀ n I, where n is number of turns per unit length and I is current. Field lines inside are nearly parallel and uniform.
An electromagnet is a soft iron core wrapped with current-carrying coil. Strength increases by increasing current, increasing turns, using a soft iron core, or winding coils tightly. Used in relays, motors, scrapyard cranes.
Fleming's left-hand rule: stretch thumb, forefinger and middle finger mutually perpendicular — forefinger = magnetic field (N→S), middle finger = current (conventional), thumb = force/motion. Force magnitude: F = I L B sinθ.
A rectangular coil in a magnetic field experiences forces on its sides creating torque; with a commutator the direction of current reverses each half-turn so torque remains unidirectional — thus electric energy converts to mechanical rotation (DC motor).
Galvanometer: coil in magnetic field deflects in proportion to current. To make an ammeter, add a low-resistance shunt in parallel to carry most current. To make a voltmeter, add a high resistance in series so only small current passes through the galvanometer.
Faraday discovered that an emf is induced in a circuit when magnetic flux through it changes. Induced emf magnitude depends on rate of change of magnetic flux and direction given by Lenz's law.
Lenz's law: the direction of induced current is such that it opposes the change in magnetic flux that produced it. It ensures conservation of energy — induced currents produce magnetic effects resisting the change.
Faraday's law: ε = - dΦ/dt, where Φ is magnetic flux through the circuit and the negative sign reflects Lenz's law (direction opposing change).
Magnetic flux through an area A with magnetic field B at angle θ: Φ = B·A·cosθ. Unit: weber (Wb).
- Move a magnet towards/away from coil (changes B through coil).
- Change area of coil or orientation relative to field (A or cosθ changes).
- Change current in nearby coil (mutual induction) altering flux.
Coil rotates in a magnetic field, changing flux through it; by Faraday's law an emf is induced that alternates as coil orientation changes. Slip rings provide alternating output. Frequency depends on rotation speed and number of poles.
DC generator uses a commutator (split ring) instead of slip rings to reverse connection every half-turn so the output is unidirectional (pulsating DC) rather than alternating.
Transformer works on mutual induction between primary and secondary coils on a magnetic core. For ideal transformer: V1/V2 = N1/N2. Step-up: N2>N1; Step-down: N2<N1. Power approx conserved (neglecting losses).
Eddy currents are circulating currents induced in conducting cores by changing magnetic fields causing heating and losses. Reduced by laminating cores (insulated sheets) to increase resistance to circulation. Eddy currents exploited in induction heating and electromagnetic braking.
- Electric motors (converting electrical to mechanical).
- Generators and alternators.
- Transformers for power distribution.
- Electromagnets in relays, cranes, MRI machines.
- Induction heating and magnetic braking.
Use Lenz's law: assume a direction that would oppose the flux change. Alternatively use right-hand rules for motional emf: force on positive charges F = q(v × B) gives direction of induced current.
Between opposite poles field lines run approximately straight from north to south. If poles are close and surfaces large, the field in the gap is nearly uniform and strong; field strength decreases with distance from poles.
For a single circular loop of radius R carrying current I, field at centre: B = μ₀ I / (2 R) (direction given by right-hand rule: thumb points along axis for current direction of curled fingers).
For a finite wire the field is weaker and depends on geometry; Biot–Savart law gives exact expression via integration. For a very long wire the field approximates B = μ₀ I /(2π r).
Two parallel currents I1 and I2 separated by distance d exert force per unit length: F/L = μ₀ I1 I2 / (2π d). Currents in same direction attract; opposite directions repel.
Place a compass near a current-carrying wire; it will align tangentially to circular field lines. Moving the compass around the wire traces concentric directions showing field orientation.
Wrap insulated copper wire around an iron nail, connect to a battery. Increase strength by increasing turns or current (use more cells) and inserting a soft iron core. Demonstrate by lifting paper clips.
Mutual induction: changing current in primary coil changes flux through nearby secondary coil, inducing emf in it. Example: transformer — alternating current in primary induces alternating emf in secondary.
AC in coil beneath cooktop creates changing magnetic field inducing eddy currents in the ferromagnetic base of pan; resistive heating of pan (not hob surface) cooks food — efficient and quick.
Transformers rely on changing magnetic flux to induce emf in secondary. DC produces steady flux after transient — no continuous changing flux → no continuous induced emf, so transformers need AC.
Use right-hand rule: point fingers in velocity (v) direction, curl towards magnetic field (B), thumb points to force on positive charge (F = q v × B). For negative charges, force reverses.
Earth's field enables compass navigation and deflects charged particles from the solar wind, forming the magnetosphere which protects the atmosphere and life from harmful radiation.
Hysteresis: lag between magnetisation and applied field due to domain realignment. Cycling magnetisation causes energy loss (hysteresis loss) in transformer cores; reduced by using low-hysteresis magnetic materials (silicon steel) and thin laminations.
Fleming's right-hand rule: thumb = motion of conductor, forefinger = magnetic field (N→S), middle finger = induced current direction. Useful to find polarity in generators.
Ferromagnetic cores increase magnetic flux density for given current (high permeability), reducing required ampere-turns and device size; choice impacts hysteresis and eddy current losses.
Magnetic force perpendicular to velocity causes circular/spiral motion: F = q v B = m v^2 / r, so radius r = m v / (q B). Basis for cyclotrons and mass spectrometers.
ΔΦ = 0.1 − 0.5 = −0.4 Wb; rate = ΔΦ/Δt = −0.4/0.2 = −2 Wb/s; magnitude of induced emf = 2 V (single turn). Sign indicates direction per Lenz's law.
Induced currents (eddy currents) in conductors flow in loops and dissipate energy as heat (I^2R losses). Managed by using laminated cores, insulating coatings, and design that minimises conductive loops.
Magnetic field B unit: tesla (T) = weber/m². Earth's field ~25–65 μT (microtesla) ≈ 0.25–0.65 gauss (1 gauss = 10⁻⁴ T). MRI machines use several tesla.
Changing flux induces emf that drives current, which dissipates energy; to change flux you must do work against the induced effects (counter emf). Conservation of energy requires input work to appear as electrical energy or heat.
Use high-permeability materials (µ-metal) to redirect magnetic flux, or use conductive enclosures to create eddy current shielding for high-frequency fields. Proper grounding and spacing reduce interference.
MRI (Magnetic Resonance Imaging) uses very strong static magnetic fields and radio waves to image internal body structures by aligning and detecting nuclear magnetic moments (mainly hydrogen). Safety considerations: fringe fields affect metal objects and implants.
Laminations (thin insulated sheets) increase resistance to eddy current paths, reducing induced circulating currents and associated heating losses while preserving magnetic coupling.
Use left-hand rule for motors (current & field → force/motion). Use right-hand rule for generators (motion & field → induced current). They are mirror concepts depending on cause/effect.
Magnetic dipole moment is a measure of strength and orientation of a magnetic source (like a bar magnet or current loop). A dipole in a uniform field experiences torque tending to align it with the field.
Drop a strong magnet through a copper pipe — it falls slower than through air due to induced currents producing magnetic force opposing motion. Alternatively moving magnet towards coil connected to bulb lights it briefly with polarity obeying Lenz's law.
Keep magnets away from pacemakers, credit cards, magnetic storage, and ferromagnetic tools. Secure heavy ferrous objects to avoid sudden attraction. Handle strong magnets carefully to prevent pinching injuries.
Maglev uses controlled magnetic attraction/repulsion (electromagnets or superconducting magnets) to lift and propel trains with minimal friction. Active control systems maintain stable levitation and guidance.
- Field around long straight wire:
B = μ₀ I /(2π r). - Field at centre of loop:
B = μ₀ I /(2R). - Solenoid:
B = μ₀ n I. - Force on conductor:
F = I L B sinθ. - Faraday:
ε = - dΦ/dt.
- Current produces magnetic fields (Oersted). Use right-hand rules to find direction.
- Coils & solenoids act like bar magnets; electromagnets and motors exploit force on currents.
- Changing flux induces emf (Faraday & Lenz) — basics for generators & transformers.
- Applications: motors, generators, transformers, induction heating, MRI, maglev — with practical safety & loss considerations.