Magnetism Lecture Notes

Introduction to Magnetism

• Common experience with magnets (e.g., playing with magnets and finding metal objects in sand)
• Bar magnet structure: has a north pole (N) and a south pole (S)

Cutting a Bar Magnet

• When you cut a bar magnet in half, each half forms a new magnet with its own N and S poles
• Cutting repeatedly always results in smaller magnets, each with N and S poles
• Key Statement: There are no magnetic monopoles (cannot have just an N or just an S pole)

Magnet vs. Electric Charge

• Magnetic poles always come in pairs (N and S together)
• Electric charges can exist independently (e.g., positive and negative charges)
• Theoretical magnetic monopoles have been proposed but not experimentally confirmed

Magnetic Forces

• Like poles repel, opposites attract
• Analogous to electrostatic forces (positive vs. negative charges)

Magnetic Field (B field) of a Bar Magnet

• Similar to electric dipole field
• Magnetic field lines (B lines) are continuous (they form closed loops)
• B field lines inside a bar magnet move from S to N internally and from N to S externally

Magnetic Force on Moving Charges

• Force equation: F = qvBsin(θ)
  • q : Charge
  • v : Velocity
  • B : Magnetic field strength
  • θ : Angle between velocity and magnetic field
  • Direction determined by the right-hand rule

Right-Hand Rule for Magnetic Force

• Fingers point in the direction of v, curl in direction of B, thumb points in the direction of the force
• If the charge is negative, the direction of the force is reversed

Magnetic Force in Different Orientations

• When a charge moves perpendicular to a magnetic field, it feels the maximum force (sin(90°) = 1)
• When parallel or antiparallel (sin(0°) = 0), there is no force
• If the B field and velocity v are not perpendicular, use sin(θ) for the angle between them

Application: Motion of Charges in B Field

• A charge moving in a magnetic field often follows a circular path
  • Radius of the circle r = mv/qB
• Centripetal force: mv²/r = qvB

Wires Carrying Current in B Fields

• Current in a wire feels a magnetic force in a magnetic field: F = ILBsin(θ)
• I : Current
• L : Length of wire
• θ : Angle between current direction and B field
• Right-hand rule: Fingers point in direction of I, curl in direction of B, thumb points in direction of force
• Force calculated on each side of a current-carrying loop, resulting in torque
• Torque on loop: τ = IABsin(φ)

Magnetic Fields Generated by Current-Carrying Wires

• A current-carrying wire produces a magnetic field around it: B = (μ₀ I) / (2πr)
  • μ₀: Permeability of free space
  • r: Distance from the wire
• Direction of B field given by another right-hand rule (thumb in direction of current, fingers curl in direction of B field)

Example Problem: Force Between Two Parallel Wires

• Wires carrying current exert forces on each other
• Example problem calculated the force and resulting current in a second wire
• Attractive or repulsive forces depend on the direction of the currents relative to each other.