Lecture on Magnetism

Basic Principles of Magnetism

• Bar magnets have a North and South Pole.
  • Like poles repel: North-North or South-South.
  • Unlike poles attract: North-South.
• Each bar magnet has its own magnetic field from North to South.
• Magnetic fields cancel or reinforce based on the direction of poles.

Creation of Magnetic Fields

• Moving electric charges create magnetic fields.
• A current through a wire generates a circular magnetic field.
• Use the right-hand rule to determine the direction of the magnetic field.
  • Thumb in direction of current, fingers show field direction.

Calculating Magnetic Field Strength

• Formula: B = μ₀I / (2πR)
  • B = magnetic field in Teslas.
  • μ₀ = permeability of free space = 4π x 10⁻⁷ T·m/A.
  • I = current in Amps.
  • R = distance from the wire in meters.
• Current (I) and magnetic field (B) are directly related; increase in I increases B.
• Distance (R) is inversely related to B; increase in R decreases B.

Magnetic Force on a Wire

• Formula: F = ILB sin(θ)
  • F = magnetic force.
  • I = current in the wire.
  • L = length of the wire.
  • B = magnetic field.
  • θ = angle between current and magnetic field.
• Maximum force when current and field are perpendicular (θ = 90°).
• No force when current and field are parallel (θ = 0°).
• Right-hand rule used to determine force direction.

Magnetic Force on a Moving Charge

• Formula: F = Bqv sin(θ)
  • q = charge of the particle.
  • v = velocity of the particle.
• Maximum force when velocity and magnetic field are perpendicular.
• Direction determined by right-hand rule for positive charges and opposite for negative charges.

Motion of Charged Particles in Magnetic Fields

• Perpendicular magnetic force causes circular motion.
• Radius of Circle Formula: r = mv / (Bq)
  • m = mass of the particle.
• Energy of a particle can be expressed in electron volts (eV).

Interaction Between Parallel Currents

• Parallel wires with currents in the same direction attract.
• Opposite directions result in repulsion.
• Force Between Wires Formula: F = μ₀I₁I₂L / (2πR)
  • I₁ & I₂ = currents in the wires.
  • L = length of the wires.

Ampère's Law and Solenoids

• Ampère's Law: ΣBΔL = μ₀I
  • Applies to closed loops.
• Solenoids generate strong internal magnetic fields.
• Solenoid Field Formula: B = μ₀nI
  • n = number of turns per unit length.

Torque on a Current Loop

• Current loops in magnetic fields experience torque.
• Torque Formula: τ = nIAB sin(θ)
  • A = area of the loop.
• Torque is maximal when magnetic field is perpendicular to loop.
• Equilibrium occurs when torque is zero, typically when magnetic field is parallel to loop normal.