Class 12 — Notes 🎯

In 1820, Danish physicist Hans Christian Oersted discovered that an electric current produces a magnetic field around it.

Experiment: A compass needle is placed near a straight wire. When current flows through the wire, the needle deflects, showing a magnetic field is created. When current is reversed, the needle deflects in the opposite direction. When current is switched off, needle returns to original position.

Observations:
(1) Current-carrying wire produces a magnetic field in its surrounding space
(2) Direction of field depends on direction of current
(3) Magnitude of field depends on the current and distance from wire

This experiment established that electricity and magnetism are interrelated — a fundamental discovery leading to electromagnetism.

Biot-Savart Law gives the magnetic field dB produced by a small current element Idl at a point P at distance r.

dB = (μ₀/4π) × (Idl sinθ)/r²

Where: μ₀ = 4π×10⁻⁷ T·m/A, θ = angle between the current element dl and the line joining dl to point P

Direction of dB: perpendicular to both dl and r̂, given by right-hand screw rule (or cross product dl × r̂).

Applications:
(1) Infinite straight wire: B = μ₀I/2πr
(2) Circular loop at centre: B = μ₀I/2R (for N turns: B = Nμ₀I/2R)
(3) Circular loop on axis at distance x: B = μ₀IR²/[2(R²+x²)^(3/2)]

Compare with Coulomb's Law: Biot-Savart is the magnetic analogue of Coulomb's law — both have 1/r² dependence, but magnetic force depends on current element (moving charge), not static charge.

Ampere's Circuital Law: The line integral of the magnetic field B along any closed path (Amperian loop) equals μ₀ times the total current enclosed by that path.
∮B·dl = μ₀I_enclosed

It is the magnetic analogue of Gauss's Law in electrostatics — useful for highly symmetric current distributions.

Solenoid: A long coil of wire with closely wound turns. Inside a long solenoid: B = μ₀nI where n = N/L = number of turns per unit length. Field inside is uniform and parallel to axis. Field outside is nearly zero.

Toroid: A solenoid bent into a closed ring. Inside the toroid: B = μ₀NI/2πr where N = total turns, r = radius of toroid. Outside the toroid: B = 0 (field confined completely inside).

Force on a current-carrying conductor in a magnetic field:
F = BIL sinθ (θ = angle between wire and B). Direction: Fleming's Left-Hand Rule.
Maximum when θ = 90° (wire ⊥ B): F = BIL. Zero when θ = 0° (wire ∥ B).

Force between two parallel current-carrying wires:
F/L = μ₀I₁I₂/2πd. Parallel currents attract; antiparallel (opposite) currents repel.
This is used to define 1 Ampere: 1 A is that current which, flowing in two infinite parallel wires 1 m apart in vacuum, produces a force of 2×10⁻⁷ N per metre between them.

Lorentz Force on a moving charge: F = qvB sinθ
Combined: F = q(E + v×B). Magnetic force does no work (⊥ to velocity).

Circular motion: In uniform B, a charged particle moves in a circle. Centripetal force = Lorentz force: mv²/r = qvB → r = mv/qB
Cyclotron frequency: f = qB/2πm — independent of speed (isochronous property used in cyclotron).

A rectangular loop of N turns, area A, carrying current I placed in uniform magnetic field B experiences a torque τ = NIAB sinθ where θ = angle between plane of loop and B (or 90°−φ where φ is angle between normal to loop and B).

Moving Coil Galvanometer (MCG): A coil is suspended between poles of a permanent magnet using a phosphor-bronze strip. A soft iron core ensures radial field (θ always 90°).

At equilibrium: Deflecting torque = Restoring torque
NIAB = kφ → φ = NIAB/k

Where k = restoring torque per unit deflection (torsional constant), φ = deflection angle.

Current sensitivity = φ/I = NAB/k
Voltage sensitivity = NAB/kR

Conversion to Ammeter: Connect a low resistance shunt S in parallel. S = Ig×G/(I−Ig)
Conversion to Voltmeter: Connect high resistance R in series. R = (V/Ig) − G