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.