Lecture Notes: Magnetism

Overview

• Magnetism Basics:
  • Bar magnets have North and South poles.
  • Like poles repel; unlike poles attract.
  • Magnetic fields emanate from the North Pole and travel towards the South Pole.
  • Magnetic fields cancel in the middle when repelling.

Origin of Magnetic Fields

• Created by Moving Electric Charges:
  • Example: A wire with electric current creates a circular magnetic field.
  • Right-hand rule: Thumb points in current direction; fingers show magnetic field direction.

Calculating Magnetic Field Strength

• Formula: $B = \frac{\mu_0 I}{2\pi r}$
  • Parameters:
    • $B$: Magnetic field strength (Tesla)
    • $\mu_0$: Permeability of free space ($4\pi \times 10^{-7}$ T·m/A)
    • $I$: Electric current (Amps)
    • $r$: Distance from the wire (meters)
  • Relationships:
    • $I$ and $B$ are directly proportional.
    • $r$ and $B$ are inversely proportional.

Magnetic Force on Current-Carrying Wires

• Formula: $F = ILB \sin(\theta)$
  • Factors:
    • Current ($I$)
    • Length of wire ($L$)
    • Magnetic field strength ($B$)
    • Angle ($\theta$) between current and magnetic field
  • Maximum Force: When current and field are perpendicular.

Calculating Magnetic Force on a Moving Charge

• Formula: $F = BQV \sin(\theta)$
  • Parameters:
    • $B$: Magnetic field (Tesla)
    • $Q$: Charge (Coulombs)
    • $V$: Velocity (m/s)
    • $\theta$: Angle between velocity and magnetic field

Motion of Charged Particles in Magnetic Fields

• Circular Motion:
  • Force acts as centripetal force.
  • Equations:
    • Centripetal Force: $F_c = \frac{mv^2}{r}$
    • Magnetic Force: $F_B = BQV$
  • Radius of Path: $r = \frac{mv}{BQ}$

Interaction Between Parallel Wires

• Same Direction: Attraction
• Opposite Direction: Repulsion
• Equation for Force Between Wires:
  • $F = \frac{\mu_0 I_1 I_2 L}{2\pi r}$

Ampere's Law

• Relates magnetic field around a current to the current itself.
• Application to Solenoids:
  • Solenoid creates a strong internal magnetic field.
  • Equation: $B = \mu_0 n I$
    • $n$: Number of turns per meter

Torque on Current-Carrying Loops

• When in Magnetic Field:
  • Torque is exerted that can cause rotation.
  • Equation: $\tau = NIAB \sin(\theta)$
    • $N$: Number of loops
    • $I$: Current
    • $A$: Area of loop
    • $B$: Magnetic field
    • Maximum torque when $\theta = 90^\circ$

Practice Problems

• Calculations for Specific Situations:
  • Example problems involving wire currents, magnetic fields, forces, and torque.