Magnetic Fields – Electromagnetism & Forces

Magnets & Magnetic Fields

  • Magnet: rock/metal that exerts attraction on iron, nickel, cobalt.
  • Magnetism: fundamental force; acts over distance.
  • Every magnet has inseparable poles (N & S).
    • Unlike poles attract; like poles repel.
    • Freely suspended magnet aligns N–S.
  • Permanent vs Temporary
    • Permanent: atomic domains aligned persistently.
    • Temporary: domains align only inside strong external B; heat/random motion destroys alignment.
  • Magnetic field: region where magnetic force is felt around magnet, magnetic object, or moving charge.

Electromagnetism

  • Discovered by Oersted (1820): current in wire deflects compass ⇒ electric current creates B.
  • Electric (electrostatic) & magnetic forces are two aspects of single electromagnetic force (attractive/repulsive between charges & magnets).

Solenoids & Electromagnets

  • Solenoid: wire coil with many loops carrying current.
    • Each loop’s field adds ⇒ strong, bar-magnet-like B (north/south ends).
  • Field strength increases with
    • Larger current I.
    • More turns N & closer spacing.
    • Ferromagnetic core (iron rod).
  • Electromagnet: magnet whose field is produced by current; polarity can be reversed by reversing current.

Right-Hand Rules (conventional current + to -)

  • First RHR (straight wire / single loop)
    • Thumb: current I direction.
    • Curled fingers: circular B direction.
  • Second RHR (solenoid / electromagnet)
    • Fingers: current around coils.
    • Thumb: north pole of electromagnet / B through core.
  • Third RHR (force on wire)
    • Index: B direction.
    • Middle: current I.
    • Thumb: magnetic force F (on positive charges). 90° to both I and B.

Force on Current-Carrying Wire

  • Magnitude: F = I L B \sin\theta
    • I: current (A)
    • L: length of wire in field (m)
    • B: magnetic field strength (T)
    • \theta: angle between I and B.
  • Special cases
    • Wire ⟂ field (\theta = 90^\circ): F = I L B (maximum).
    • Wire ∥ field (\theta = 0^\circ): F = 0.
  • Direction found with Third RHR; reverses if current reverses.

Quick Problem Strategy

  1. Draw I, B, identify \theta.
  2. Use F = I L B \sin\theta.
  3. Ensure units: A, m, T ⇒ F in N.
  4. For solenoids/electromagnets, apply 1st & 2nd RHR to find B direction, then 3rd RHR for F.

Key Equations & Units

  • F = I L B \sin\theta ( N )
  • Symbols: F force (N); I current (A); L length (m); B field (T); \theta angle (°).
  • Remember: 1\,\text{T} = 1\,\text{N}\,\text{s}/(\text{C}\,\text{m}) in SI.