Physics Notes on Electricity and Magnetism

Lesson 1: Prefinals

Differentiating Electricity and Magnetism

  • Geographic North & Magnetic South:

    • Map magnetic poles:
      Geographic North (N) corresponds to Magnetic South (S).

    • Magnetic Polarity: Typically represented as + for North and - for South.

Basic Physics Principles

  • Force formulas and relationships:

    • Magnetic force: Fm=qimesvimesBimesextsinhetaF_{m} = q imes v imes B imes ext{sin} heta

    • Gravitational force: F<em>g=racGimesm</em>1imesm2r2F<em>{g} = rac{G imes m</em>1 imes m_2}{r^2}

    • Electric force: F<em>e=racKimesQ</em>1imesQ2r2F<em>e = rac{K imes Q</em>1 imes Q_2}{r^2}

    • Common physical quantities:

    • m = mass,

    • q = charge,

    • B = magnetic field (in tesla),

    • I = current (in amperes).

Understanding Magnetism

  • Definition: Magnetism refers to the force applied by magnets, which attract or repel each other based on their poles.

  • Cause of magnetism: Result of interactions between electrons in objects.

Historical Context

  • In 1820, Hans Christian Oersted demonstrated that moving charges produce a magnetic field by moving current through a wire affecting a compass needle.

Key Formulas for Forces

  • Fm=BILextsinhetaF_m = BIL ext{sin} heta (Force on a wire carrying current in a magnetic field)

  • I=racFmBLextsinhetaI = rac{F_m}{BL ext{sin} heta}

  • Units of Measurement:

    • SI unit for magnetic field: Tesla (T)

    • Another unit: Gauss (G) = 1extG=10−4T1 ext{G} = 10^{-4} T

    • Force: measured in Newtons (N).

Magnetic Force Calculations

  1. Example 1:
    An 8.12 μC charge with speed 40.0 m/s in a 0.75 T field:
    Fm=(8.12imes10−6extC)(40.0extm/s)(0.75)=2.436imes10−4extNF_m = (8.12 imes 10^{-6} ext{C}) (40.0 ext{m/s}) (0.75) = 2.436 imes 10^{-4} ext{N}

  2. Example 2:
    A 7.55 μC charge, 30.50 m/s, 1.2 T:
    Fm=(7.55imes10−6)(30.50)(1.2)=2.2633imes10−4extNF_m = (7.55 imes 10^{-6}) (30.50) (1.2) = 2.2633 imes 10^{-4} ext{N}

  3. Wire Examples:

    • Calculate magnetic field from current:

    • For a 100-cm wire carrying 0.25 A with 5.50 X 10^{-3} N force:
      B=racFmILextsinhetaB = rac{F_m}{IL ext{sin} heta}
      B=rac5.50imes10−3(0.25)(1)=0.022extTB = rac{5.50 imes 10^{-3}}{(0.25)(1)} = 0.022 ext{T}

Induced Current in Loops and Resistances

  • Induction Basics: Changes in magnetic fields induce current.

  • Examples of induced emf calculation in loops

    • Factors include area, resistance, and angle of rotation relative to the magnetic field.

    • Example formulas include Faraday's Law: extElectromotiveForce(emf)=−racextdextFluxextdtext{Electromotive Force (emf)} = - rac{ ext{d} ext{Flux}}{ ext{dt}}

Lesson 2: Biot-Savart Law

  • Magnetic Force Fundamentals:

    • Magnetic field around a current-carrying wire increases with current and is determined by the distance from the wire.

    • For two parallel wires: F/extlength=racextconstantimesI<em>1imesI</em>2extdistanceF/ ext{length} = rac{ ext{constant} imes I<em>1 imes I</em>2}{ ext{distance}}

Applications of Biot-Savart Law

  • Calculate the magnetic fields generated by various current configurations and use principles to find forces between currents.

Maxwell's Equations

  • Fundamental laws of electromagnetism:

    1. Gauss's Law for Electricity ( ext{Electric Flux} = rac{Q}{ ext{Permitivity}})

    2. Gauss's Law for Magnetism (Net Magnetic Flux = 0)

    3. Faraday's Law (Induced Electric Field from Changing Magnetic Field)

    4. Ampere's Law (Magnetic Field from Electric Current)

Conclusion

  • These principles and equations form the foundation of the behaviour of electric and magnetic fields and their interactions, vital for understanding electromagnetism in both theoretical and practical contexts.