Magnetism Lecture Notes

Basics of Magnetism

• Bar Magnets:
  • North pole repels another north pole.
  • North pole attracts a south pole.
  • South pole repels another south pole.
• Magnetic Field:
  • Emanates from the north pole to the south pole.
  • Magnetic fields cancel out when poles repel.
  • Magnetic fields align and add up when poles attract.

Magnetic Fields and Electric Currents

• Creation of Magnetic Fields:
  • Caused by moving electric charges.
  • Example: A current through a wire creates a circular magnetic field.
• Right-Hand Rule:
  • Thumb points in the direction of current.
  • Fingers curl in the direction of magnetic field.

Calculating Magnetic Field Strength

• Formula: B = μ₀ * I / (2πR)
  • B: Magnetic field strength (Tesla)
  • μ₀: Permeability of free space ( $4π × 10^{-7} T·m/A)$
  • I: Current (Amperes)
  • R: Distance from the wire (meters)
• Relationship:
  • Increasing current increases magnetic field strength.
  • Increasing distance decreases magnetic field strength.*

Magnetic Force on a Wire

• Formula: F = I * L * B * sin(θ)
  • F: Force (Newtons)
  • L: Length of the wire in the field (meters)
  • θ: Angle between current and magnetic field
• Force Direction:
  • Use right-hand rule: thumb in current direction, fingers in field direction, force comes out from palm.*

Magnetic Force on Charge

• Formula: F = B * q * v * sin(θ)
  • q: Charge (Coulombs)
  • v: Velocity (m/s)
• Direction & Behavior:
  • Perpendicular force results in circular motion.
  • Opposite charges experience force in opposite directions.*

Current-Carrying Wire in Magnetic Field

• Force Between Wires:
  • Attraction if currents are in the same direction.
  • Repulsion if currents are in opposite directions.
• Formula for Force Between Wires:
  • F = μ₀ * I₁ * I₂ * L / (2πR)*

Ampere’s Law

• Relationship:
  • Describes the magnetic field in terms of a current enclosed by a path.
• Equation for Wire:
  • B = μ₀ * I / (2πR) derived from Ampere’s law.*

Solenoids

• Definition: Device with many loops of wire to intensify magnetic field.
• Formula for Magnetic Field:
  • B = μ₀ * n * I
  • n: Number of loops per meter
• Effect of Parameters:
  • Increase current or loops for stronger field.
  • Decrease length for stronger field.

Torque on a Loop in a Magnetic Field

• Formula: τ = n * I * A * B * sin(θ)
  • τ: Torque (Newton-meters)
  • A: Area of loop (square meters)
• Torque Behavior:
  • Maximum when magnetic field is parallel to coil's face.
  • Zero torque when magnetic field is perpendicular to coil face.

Practical Example Problems

• Magnetic Field Strength & Direction:
  • Calculated using given current, distance, and wire orientation.
• Force and Torque Calculations:
  • Solved using the formulas for force between wires and torque on coils.
• Energy and Motion of Particles:
  • Understanding of how charged particles move in magnetic fields.

These notes cover the fundamental concepts and equations related to magnetism discussed in the lecture, providing a basis for further study and problem-solving in physics.