This chapter explores electromagnetic waves, which are crucial for understanding light and communications.
ELECTROMAGNETIC WAVES – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the ELECTROMAGNETIC WAVES chapter of Physics Part - I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
E = mc²
E is energy (in joules), m is mass (in kg), and c is the speed of light (≈ 3 × 10⁸ m/s). Mass-energy equivalence illustrates conversion of mass to energy.
c = λν
c is the speed of light (3 × 10⁸ m/s), λ is wavelength (in meters), and ν is frequency (in Hz). This relates the speed, frequency, and wavelength of electromagnetic waves.
ν = ω/2π
ν is frequency (Hz), and ω is the angular frequency (radians/second). Conversion between frequency and angular frequency is common in wave mechanics.
k = 2π/λ
k is the wave number (radians/m), and λ is the wavelength (in meters). It describes the spatial frequency of a wave.
B₀ = E₀/c
B₀ is the amplitude of the magnetic field (T), E₀ is the amplitude of the electric field (V/m), and c is the speed of light (≈ 3 × 10⁸ m/s). This relation indicates the relationship between electric and magnetic fields in an electromagnetic wave.
dΦ_E/dt = ε₀(i + i_d)
Φ_E is electric flux, ε₀ is permittivity of free space, i is conduction current (A), and i_d is displacement current. This is a generalization of Ampere's Law considering displacement current.
ω = ck
ω is the angular frequency (radians/second), c is the speed of light (≈ 3 × 10⁸ m/s), and k is the wave number (radians/m). This relates frequency and wavelength to wave speed.
Φ_B = ∫ B ⋅ dA
Φ_B is the magnetic flux (Webers), B is the magnetic field (T), and A is area (m²). This equation assesses the magnetic field passing through a surface area.
E = hν
E is energy of a photon (J), h is Planck's constant (6.626 × 10⁻³⁴ J·s), and ν is frequency (Hz). This quantifies the energy level of electromagnetic radiation.
v = 1/√(εμ)
v is the velocity of electromagnetic waves in a medium, ε is permittivity, and μ is permeability. This provides the relationship governing speed based on medium properties.
Equations
Gauss's Law (Electric Field): ∮ E ⋅ dA = Q/ε₀
E is electric field (N/C), dA is differential area vector (m²), Q is charge (C), and ε₀ is permittivity of free space. This law relates electric field to charge.
Gauss's Law (Magnetic Field): ∮ B ⋅ dA = 0
B is magnetic field (T), dA is differential area vector (m²). This law states that there are no magnetic monopoles; hence, the net magnetic flux through a closed surface is zero.
Faraday's Law: ∮ E ⋅ dl = -dΦ_B/dt
E is electric field, dl is differential length, and Φ_B is magnetic flux (Webers). This law quantifies the electromotive force induced by a changing magnetic field.
Ampere-Maxwell Law: ∮ B ⋅ dl = μ₀(i + ε₀ dΦ_E/dt)
B is magnetic field, dl is differential length, μ₀ is permeability of free space, i is conduction current, and dΦ_E/dt is rate of change of electric flux. It generalizes Ampere's law to include the displacement current.
Wave Equation: ∇²E = (1/c²)(∂²E/∂t²)
∇²E is Laplacian of electric field, ∂²E/∂t² is second temporal derivative of electric field, and c is speed of light. This is the wave equation governing electromagnetic waves.
Power carried by an EM wave: P = (1/2)ε₀E₀²cA
P is power (W), E₀ is amplitude of electric field (V/m), c is speed of light (m/s), and A is area (m²). This equation calculates the power transmitted by an electromagnetic wave.
This chapter discusses the concept of electric current, its laws, and the behavior of currents in various materials, particularly in conductors.
Start chapterThis chapter discusses the relationship between moving charges and magnetic fields. It is crucial for understanding how electric currents generate magnetic fields and the effects of these fields on charged particles.
Start chapterThis chapter explores the fundamentals of magnetism and its interaction with matter, highlighting the principles and types of magnetic materials.
Start chapterThis chapter explores alternating current, a common form of electric power. It highlights its importance in daily life, especially in powering devices and its advantages over direct current.
Start chapter
