Moving Charges & Magnetism

• Evaluate magnetic Lorentz force: F = q(v × B) and helical particle trajectories.
• Apply Biot-Savart law to derive magnetic field on circular loop axes.
• Apply Ampere's circuital law to infinite wires, long solenoids, and toroids.
• Explain the operational principle and conversion of a Moving Coil Galvanometer into an ammeter/voltmeter.

• Magnetic Force on Moving Charge (F = q(E + v × B))
• Biot-Savart Law (dB = (μ0/4π) (I dl × r̂ / r^2))
• Ampere's Circuital Law (∮ B · dl = μ0 I_enclosed)
• Force between Two Parallel Current Wires (Definition of Ampere)
• Torque on Current Loop (τ = M × B) & Magnetic Dipole Moment (M = NIA)
• Moving Coil Galvanometer Conversion (Shunt & Series Multiplier)

“Magnetic forces do no work on moving charges because force is always perpendicular to velocity (v · F = 0).”

• •Magnetic field at center of circular coil: B = μ0 I / (2R); along axis: B = μ0 I R^2 / (2(R^2+x^2)^(3/2)).
• •Two parallel currents attract if in the same direction, repel if opposite.
• •To convert galvanometer to ammeter, connect small shunt resistance in parallel.

Rigorous problems on Biot-Savart field integrals, galvanometer conversions, and helical particle orbits.