Magnetism Lecture Notes 🔍

Bar Magnets

• Poles Interaction:
  • Like poles repel (North-North or South-South)
  • Opposite poles attract (North-South)
• Magnetic Fields:
  • Emanate from the North pole and travel to the South pole
  • Fields cancel in the middle when poles repel; align and add up when poles attract

Magnetic Fields and Electric Currents

• Creation of Magnetic Fields:

  • Created by moving electric charge
  • Example: Current-carrying wire

• Magnetic Field around a Wire:

  • Circular magnetic field
  • Right-hand rule: Thumb points in current direction; fingers curl in the direction of the magnetic field
  • Magnetic field strength formula:
    • B = μ0 * I / (2π * r)
    • μ0 = 4π * 10^(-7) T*m/A (permeability of free space)
    • r is the distance from wire

Calculations and Examples

Example 1

• Given: Straight wire, current = 45 A, distance = 2 cm
• Direction: Right-hand rule (dot/cross notation)
• Magnitude Calculation: Use the formula
  • B = (4π * 10^(-7) * 45) / (2π * 0.02) = 4.5 * 10^(-4) T

Example 2

• Given: Wire with current = 10 A, magnetic field = 8 * 10^(-4) T

• Finding Distance r: Rearrange formula, solve for r

  • r = (4π * 10^(-7) * 10) / (2π * 8 * 10^(-4)) = 2.5 * 10^(-3) m

• Direction and Deflection: Compass deflection when near a current-carrying wire

Magnetic Force on a Current-Carrying Wire

• Force Formula: F = I * L * B * sin(θ)
• Dependence:
  • Directly proportional to I, B, and L
  • Angle between current and magnetic field matters
  • Max force when θ = 90°
  • No force when θ = 0° (parallel)

Example 3

• Given: Wire length = 2.5 m, current = 5 A, magnetic field = 2 * 10^(-3) T, θ = 30°
• Calculation: F = 5 * 2.5 * 2 * 10^(-3) * sin(30) = 0.0125 N

Example 4

• Given: Current = 35 A, force per meter = 0.75 N/m, magnetic field = directed south

• Finding B: B = 0.75 / 35 = 0.0214 T

• Direction of magnetic force using right-hand rule

Moving Charges in Magnetic Fields

• Force on Moving Charge: F = B * q * v * sin(θ)
  • Max force when θ = 90°
  • No force when θ = 0°

Example 5

• Given: Proton velocity = 4 * 10^6 m/s, magnetic field = 2 * 10^(-4) T, θ = 90°
• Calculation: F = 2 * 10^(-4) * 1.6 * 10^(-19) * 4 * 10^6 = 1.28 * 10^(-16) N

Radius of Curvature

• Equation: Set centripetal force equal to magnetic force
  • F_c = m * v^2 / r = B * q * v
  • Solving for r: r = m * v / (B * q)

Example 6

• Given: Proton velocity = 5 * 10^6 m/s, magnetic field = 2.5 T
• Calculation: r = m * v / (B * q) = 1.673 * 10^(-27) * 5 * 10^6 / (2.5 * 1.6 * 10^(-19)) = ~2.09 cm

Ampère's Law and Solenoids

• Magnetic Field Around a Wire: B = μ0 * I / (2π * r)
• Solenoid: Produce strong internal magnetic fields
  • Equation: B = μ0 * (N/l) * I
  • N/l: Turns per meter

Example 8

• Given: Solenoid length = 15 cm, turns = 800, current = 5 A
• Calculation: N/l = 800/0.15 = ~5333 turns/m
  • B = 4π * 10^(-7) * 5333 * 5 = 0.0335 T

Forces Between Parallel Currents

• Force Formula: F2 = I2 * L * B1
• Force Between Two Wires: B1 = μ0 * I1 / (2π * r)
  • Total Force: F = μ0 * I1 * I2 * L / (2π * r)

Example 7

• Given: Wire length = 30 m, distance = 2 cm, current = 50 A
• Calculation: F = 4π * 10^(-7) * 50^2 * 30 / (2π * 0.02) = 0.75 N

Rotating Current Loops in Magnetic Fields

• Torque Formula: T = N * I * A * B * sin(θ)
  • Max torque when θ = 90°
  • No torque when θ = 0°

Example 9

• Given: Coil radius = 30 cm, loops = 50, current = 8 A, magnetic field = 5 T, max angle
• Calculation: A = π * (0.3)^2 = 0.2827 m^2
  • T = 50 * 8 * 0.2827 * 5 = 565.5 Nm

Example 10

• Given: Rectangular loop, loops = 200, current = 15 A, torque = 1200 Nm, area = 0.2 m²
• Finding B: N * I * A * B = 1200
  • B = 1200 / (200 * 15 * 0.2) = 2 T

Final Summary

• Understanding Right-hand Rule: Crucial for determining direction of magnetic fields and forces
• Important Formulas: Know and understand how to use the different equations for magnetic fields, forces, and torque, including practical examples

Feel free to check the lecture or video for any clarifications. Happy studying!