Magnetic Effects of Current and Magnetism
Why This Chapter Matters
Magnetism gives 8-10 marks in CBSE Class 12. Biot-Savart law, Ampere's law, force on conductor, moving coil galvanometer, and bar magnet are all standard board topics.
Core Concepts
1. Biot-Savart Law
dB = (μ₀/4π)(Idl sinθ/r²)
Direction: right-hand curl rule (thumb = current, fingers = B direction).
Key results:
Circular loop (at centre): B = μ₀I/2R
Infinite straight wire: B = μ₀I/2πd (d = perpendicular distance)
Solenoid (inside): B = μ₀nI (n = turns per unit length)
2. Ampere's Circuital Law
∮B⃗·dl⃗ = μ₀I_enclosed
Used to find B for symmetric distributions.
Inside toroid: B = μ₀NI/2πr. Outside toroid: B = 0.
3. Force on Moving Charge
Lorentz force: F = q(v⃗×B⃗) = qvBsinθ
Magnetic force does no work (always ⊥ to velocity).
Circular motion: r = mv/qB, T = 2πm/qB (period independent of speed).
4. Force on Current Conductor
F = I(L⃗×B⃗) = BILsinθ
Direction: Fleming's left-hand rule (FBI rule).
Force per unit length between parallel wires: F/L = μ₀I₁I₂/2πd
Same direction → attractive. Opposite → repulsive.
1 Ampere defined from this: force = 2×10⁻⁷ N/m when I₁=I₂=1A, d=1m.
5. Torque on Current Loop
τ = NIAB sinθ = M×B sinθ
M = NIA = magnetic dipole moment (A·m²).
For loop in uniform field: τ = MB sinθ. Equilibrium when θ=0 or 180°.
Potential energy: U = -MB cosθ.
6. Moving Coil Galvanometer
Galvanometer: measures small currents. Principle: torque on current loop.
Torque = kφ (k = torsional constant, φ = deflection angle).
At equilibrium: NIAB = kφ → φ = (NAB/k)I ∝ I. Sensitive to current.
Conversion to Ammeter: low resistance shunt S in parallel.
I_g × G = (I-I_g) × S → S = I_g × G/(I-I_g)
Conversion to Voltmeter: high resistance R in series.
V = I_g(G+R) → R = V/I_g - G.
7. Magnetism — Bar Magnet
Magnetic dipole moment: M = m × 2l (m = pole strength, 2l = length).
Axial field: B = μ₀(2M)/4πd³
Equatorial field: B = μ₀M/4πd³
At distance d: Axial = 2 × Equatorial.
Earth's magnetism:
Magnetic declination: angle between geographic and magnetic meridians.
Dip (Inclination): angle B makes with horizontal (0° at equator, 90° at poles).
Horizontal component: H = Bcosδ. Vertical: V = Bsinδ. tanδ = V/H.
Board Examples
Q1: Calculate force between two parallel wires, 2m apart, carrying 5A and 8A in same direction.
F/L = μ₀×5×8/(2π×2) = 4π×10⁻⁷×40/(4π) = 4×10⁻⁶ N/m. Attractive.
Q2: A galvanometer of resistance 50Ω gives full-scale deflection at 5mA. Convert to voltmeter reading up to 10V.
R = V/I_g - G = 10/(5×10⁻³) - 50 = 2000-50 = 1950Ω.
PYQs (CBSE)
CBSE 2023: Define magnetic declination and dip. Where on Earth is dip 0° and where is 90°?
Declination: angle between true north and magnetic north.
Dip: angle between Earth's total field and horizontal. Dip=0° at magnetic equator. Dip=90° at magnetic poles.
CBSE 2022: A circular coil of 100 turns, radius 10cm, carries 5A. Find magnetic field at centre.
B = μ₀NI/2R = (4π×10⁻⁷×100×5)/(2×0.1) = 2π×10⁻³ = 3.14×10⁻³ T ≈ π mT.