Overview
This lecture covers the fundamentals of magnetism, including magnetic fields, forces on currents and charges, the right-hand rule, calculations involving magnetic fields, Ampère's Law, solenoids, torque on loops, and applications to exam-type problems.
Magnetic Poles and Fields
- Like magnetic poles repel; unlike poles attract.
- Magnetic field lines exit the north pole and enter the south pole of a magnet.
- Magnetic fields are additive between unlike poles and cancel between like poles.
Magnetic Fields from Currents
- Moving electric charges (current) create magnetic fields.
- The magnetic field (B) around a straight wire: B = μ₀I / (2πr).
- μ₀ (permeability of free space) = 4π × 10⁻⁷ T·m/A.
- B is measured in teslas (T); increases with current, decreases with distance.
Right-Hand Rule
- Thumb points with current; fingers curl in direction of magnetic field around wire.
- For force on a wire: thumb = current, fingers = field, palm = force direction.
Magnetic Force on Wires and Charges
- Force on a wire: F = I L B sinθ (I = current, L = length, B = field, θ = angle).
- Maximum force when current and field are perpendicular; zero when parallel.
- Force on a moving charge: F = q v B sinθ (q = charge, v = speed).
- Direction: right-hand rule; for electrons, reverse direction.
Circular Motion in Magnetic Fields
- Charged particles in a magnetic field move in circles if v ⊥ B.
- Centripetal force: q v B = m v² / r ⇒ r = m v / (q B).
- Magnetic force acts as centripetal force for the motion.
Parallel Wires and Magnetic Forces
- Parallel currents attract; antiparallel currents repel.
- Force per unit length between parallel wires: F/L = μ₀I₁I₂ / (2πr).
Ampère’s Law
- ∑(B · dl) around a closed loop = μ₀ × current enclosed.
- For long straight wire: recovers B = μ₀I / (2πr).
Solenoids
- Solenoid: coil of wire; strong uniform field inside.
- Magnetic field: B = μ₀ n I (n = turns per meter, I = current).
- Increase B by raising turns, increasing current, or shortening solenoid.
Torque on Current Loops
- Torque on loop: τ = n I A B sinθ (n = loops, A = area, θ = angle with field).
- Maximum torque when plane of loop is parallel to field (θ = 90°).
- No torque when field is perpendicular to plane of loop (θ = 0°).
Key Terms & Definitions
- Magnetic Field (B) — Region around a magnet or current where magnetic forces are felt.
- μ₀ (Permeability of Free Space) — Physical constant, 4π × 10⁻⁷ T·m/A.
- Tesla (T) — SI unit of magnetic field strength.
- Right-Hand Rule — Determines magnetic field or force direction using hand orientation.
- Solenoid — Coil of wire designed to produce a uniform magnetic field.
- Torque (τ) — Tendency of a force to rotate an object about an axis.
- Ampère’s Law — Relates magnetic field in a loop to the current it encloses.
- Electron Volt (eV) — Energy gained by an electron through a potential difference of 1 volt; 1 eV = 1.6 × 10⁻¹⁹ J.
Action Items / Next Steps
- Practice applying the right-hand rule to different scenarios.
- Solve provided magnetic field and force calculation problems.
- Review definitions and memorize key equations.
- Read textbook sections on Ampère's law and solenoids.