Overview
This lecture covers the key concepts and formulas related to moving charges and magnetism, focusing on Biot-Savart Law, magnetic field due to currents, motion of charged particles in magnetic fields, and the working of galvanometers, ammeters, and voltmeters.
Introduction to Moving Charges & Magnetism
- Electrodynamics studies the effects and interactions of moving electric charges.
- Flowing electric current produces magnetic fields around conductors.
- Three effects of electric current: heating, chemical, and magnetic (focus of this chapter).
Oersted’s Experiment & Magnetic Field Around a Conductor
- Hans Christian Oersted discovered that current in a wire deflects a nearby magnetic compass.
- Magnetic field is produced around a current-carrying conductor.
Biot-Savart Law
- Biot-Savart Law gives the magnetic field produced by a small current element at a point.
- Magnetic field (dB) ∝ current (I), length element (dl), sinθ, and inversely ∝ distance squared (r²).
- Vector form: d𝐵 = (μ₀/4π) * (I d𝐥 × r̂) / r²
- μ₀ (permeability of free space) = 4π × 10⁻⁷ T·m/A.*
Magnetic Field Due to Conductors & Loops
- At the center of a circular loop: B = (μ₀ I) / (2r), for n turns: B = (μ₀ n I) / (2r)
- On the axis of a circular loop: B = (μ₀ n I r²) / [2(r² + a²)^(3/2)], where a = axial distance.
Ampere’s Circuital Law & Applications
- Ampere’s Law: ∮𝐁·d𝐥 = μ₀ n I (line integral of B around a closed loop equals μ₀ times net current enclosed).
- For a long straight wire: B = (μ₀ I) / (2πr)
- For a solenoid (long coil): B = μ₀ n I (inside, field is uniform).
Motion of Charged Particles in Magnetic Fields
- Force on moving charge: F = q(𝐯 × 𝐁) = qvB sinθ.
- If θ = 0° or 180°, F = 0 (no force, particle goes straight).
- If θ = 90°, F = qvB (maximum, circular motion).
- Radius of particle path: r = (mv)/(qB); time period: T = (2πm)/(qB).
- Kinetic energy of particle remains constant in a magnetic field.
Force on a Current-Carrying Conductor in a Magnetic Field
- Force: F = I (𝐥 × 𝐁), maximum when 𝐥 ⊥ 𝐁.
- Parallel wires carrying current exert force: F/l = (μ₀ I₁ I₂)/(2πd).
Torque on Current Loop & Galvanometer
- Torque on rectangular coil: τ = n B I A sinθ (n=number of turns, B=field, I=current, A=area, θ=angle).
- Galvanometer: device to detect small currents, works on principle of torque on a coil in magnetic field.
- Uniform/radial magnetic field ensures constant torque and linear scale.
Conversion of Galvanometer to Ammeter and Voltmeter
- Ammeter: connect low resistance (shunt) in parallel to galvanometer; ideal ammeter = zero resistance.
- Voltmeter: connect high resistance in series to galvanometer; ideal voltmeter = infinite resistance.
- Current sensitivity = deflection per unit current; voltage sensitivity = deflection per unit voltage.
Key Terms & Definitions
- Electrodynamics — Study of moving electric charges.
- Magnetic field (B) — Region around a magnet or current-carrying conductor where magnetic force is felt.
- Biot-Savart Law — Law describing magnetic field due to a small current element.
- Permeability (μ₀) — Measure of ability to support magnetic field in space.
- Ampere’s Law — Line integral of magnetic field equals μ₀ times enclosed current.
- Galvanometer — Device for detecting/measuring small electric currents.
- Shunt — Low resistance used in parallel to make an ammeter.
- Radial Magnetic Field — Magnetic field directed along the radius at every point.
Action Items / Next Steps
- Review Biot-Savart Law and practice applying it to different geometries.
- Practice derivations for field due to circular loop and solenoid.
- Solve numerical problems involving charged particle motion in magnetic fields.
- Read textbook sections on galvanometers, ammeters, and voltmeters.
- Attempt end-of-chapter questions, especially derivations and conceptual cases.