PhysicsPHY 08
Moving Charges & Magnetism
Lorentz force, Biot-Savart law, Ampere's law, cyclotron, moving coil galvanometer
Concept Core
Essential theory — everything NCERT tests on Moving Charges & Magnetism
LORENTZ FORCE & MOTION IN FIELDS
F = q(E + v×B). Magnetic force: F = qvB sinθ. Maximum when v⊥B (θ=90°). Zero when v∥B.
Circular motion in uniform B: r = mv/(qB). Time period T = 2πm/(qB) — independent of speed and radius.
Velocity selector: qE = qvB → v = E/B (only that speed passes undeflected).
BIOT-SAVART LAW
dB = (μ₀/4π) × (Idl sinθ)/r²
Field at centre of circular loop: B = μ₀I/(2R).
Infinite straight wire: B = μ₀I/(2πd).
Solenoid (interior): B = μ₀nI. Toroid: B = μ₀NI/(2πr).
AMPERE'S LAW
∮B·dl = μ₀Ienc. Applies to symmetric current distributions.
Force between parallel wires: F/L = μ₀I₁I₂/(2πd). Same direction = attract; opposite = repel. (Definition of Ampere).
CYCLOTRON & GALVANOMETER
Cyclotron: accelerates charged particles using alternating electric field + perpendicular magnetic field. Max KE = q²B²R²/(2m). Cyclotron frequency = qB/(2πm) — independent of speed.
Moving coil galvanometer: deflection θ = BANI/(k). Current sensitivity = BAN/k. Voltage sensitivity = BAN/(kR).
MAGNETISM IN MATTER
Diamagnetic: weakly repelled (Cu, Bi, Ag, water, N₂). χ small negative. μr < 1.
Paramagnetic: weakly attracted (Al, Na, Mn, O₂). χ small positive. Curie law: χ ∝ 1/T.
Ferromagnetic: strongly attracted (Fe, Co, Ni). Large χ. Hysteresis loop. Above Curie temp → paramagnetic.
Fact & Formula Vault
High-yield facts, numbers, and formulas
Key Formulae
F = qvB sinθ
r = mv/qB (circular)
T = 2πm/qB (independent of v)
B_wire = μ₀I/2πd
Magnetic Fields
Centre of loop: B = μ₀I/2R
Solenoid: B = μ₀nI
Toroid: B = μ₀NI/2πr
Force/length: F/L = μ₀I₁I₂/2πd
Magnetic Materials
Diamagnetic: χ < 0, repelled
Paramagnetic: χ > 0, attracted
Ferromagnetic: large χ, hysteresis
Curie law: χ ∝ 1/T (paramagnetic)
Worked Examples
NEET-style questions solved step-by-step
EASYTwo parallel wires carrying currents in the same direction:▾
Two parallel wires carrying currents in the same direction:
Attract each other. Force per unit length = μ₀I₁I₂/(2πd). This fact is used to define the Ampere (SI unit).
MEDIUMA proton enters a magnetic field B perpendicular to its velocity. What is its path?▾
A proton enters a magnetic field B perpendicular to its velocity. What is its path?
Magnetic force = centripetal force. Path is a circle. r = mv/(qB). Period T = 2πm/(qB) — independent of velocity. Kinetic energy is unchanged (magnetic force ⊥ velocity).
HARDCyclotron cannot accelerate electrons because:▾
Cyclotron cannot accelerate electrons because:
In a cyclotron, the oscillator frequency must match the cyclotron frequency qB/(2πm). Electrons become relativistic at low speeds → mass increases → frequency changes → resonance condition fails.
Mistake DNA
Common NEET traps for this chapter
⚠ Cyclotron period and speed
Cyclotron period T = 2πm/qB is independent of speed. This is why it can accelerate particles repeatedly. But fails for relativistic speeds.
✓ Fix: T_cyclotron independent of v — key NEET fact
⚠ Diamagnetic vs Paramagnetic examples
Common mix-up: O₂ is paramagnetic (not diamagnetic). N₂ is diamagnetic. Water is diamagnetic. Al, Na are paramagnetic. Fe, Co, Ni are ferromagnetic.
✓ Fix: O₂ = paramagnetic. N₂ = diamagnetic. Fe = ferromagnetic.
⚠ Magnetic force does no work
Since magnetic force is always ⊥ to velocity, it does NO work → KE unchanged → speed unchanged in magnetic field only.
✓ Fix: B-field: changes direction, not speed. No work done.
Chapter Intelligence
Exam data and last-minute strategy
NEET Frequency
3–4 Q/year. r = mv/qB, force between wires, cyclotron frequency, solenoid B field, magnetic material properties are standard.
High-Yield
F = qvB. r = mv/qB. T = 2πm/qB (independent of v). Parallel wires same dir = attract. Solenoid B = μ₀nI. Cyclotron can't do electrons (relativistic).
Strategy
Memorise all magnetic field formulae for wire, loop, solenoid. Practice r and T calculations. Know 2–3 examples each of dia/para/ferromagnetic materials.
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