Physics · Electromagnetism

Electromagnetic Waves formulas for JEE

Every Electromagnetic Waves formula you need for JEE, grouped by concept.

FormulasRevision notes
25 formulas1 concepts
01Electromagnetic Waves
01

Electromagnetic Waves

25 formulas

Angular Frequency

ω=2πν=2πT\omega = 2\pi\nu = \frac{2\pi}{T}

Relationship between angular frequency, linear frequency, and time period.

angular_frequencyfrequency

Displacement Current

id=ϵ0dΦEdti_d = \epsilon_0 \frac{d\Phi_E}{dt}

Maxwell's displacement current equivalent to the rate of change of electric flux.

applies whenRegions with time-varying electric fields (e.g., between capacitor plates).
displacement_currentmaxwell

Electric Flux

ΦE=∫E⋅dA\Phi_E = \int \mathbf{E} \cdot d\mathbf{A}

Definition of electric flux used in deriving displacement current.

applies whenUniform or varying electric field.
fluxelectric_field

Total Average Energy Density

uavg=12ϵ0E02=12μ0B02=E0B02μ0cu_{avg} = \frac{1}{2}\epsilon_0 E_0^2 = \frac{1}{2\mu_0} B_0^2 = \frac{E_0 B_0}{2\mu_0 c}

Total average energy density stored equally in electric and magnetic fields.

applies whenHarmonic plane wave in vacuum.
energy_densityaveragejee-advanced

Magnetic Energy Density

uB=12μ0B2u_B = \frac{1}{2\mu_0} B^2

Instantaneous energy density of the magnetic field in an EM wave.

applies whenVacuum/free space.
energy_densitymagneticjee-advanced

Electric Energy Density

uE=12ϵ0E2u_E = \frac{1}{2}\epsilon_0 E^2

Instantaneous energy density of the electric field in an EM wave.

applies whenVacuum/free space.
energy_densityelectricjee-advanced

Electric and Magnetic Field Relation

B0=E0corE0=cB0B_0 = \frac{E_0}{c} \quad \text{or} \quad E_0 = c B_0

Relationship between the amplitudes (or RMS values) of the electric and magnetic fields in free space.

applies whenVacuum/free space.
amplitudefield_relation

Intensity of EM Wave

I=⟨S⟩=uavgc=12cϵ0E02=cB022μ0I = \langle S \rangle = u_{avg} c = \frac{1}{2} c \epsilon_0 E_0^2 = \frac{c B_0^2}{2\mu_0}

Time-averaged power per unit area, equal to the magnitude of the average Poynting vector.

applies whenHarmonic plane wave in vacuum.
intensityaverage_powerjee-advanced

Gauss's Law for Electricity

∮E⋅dA=Qϵ0\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q}{\epsilon_0}

First of Maxwell's equations relating electric flux through a closed surface to enclosed charge.

applies whenVacuum/free space.
maxwellgausselectrostatics

Gauss's Law for Magnetism

∮B⋅dA=0\oint \mathbf{B} \cdot d\mathbf{A} = 0

Second of Maxwell's equations implying the non-existence of magnetic monopoles.

applies whenAlways valid.
maxwellgaussmagnetism

Faraday's Law of Induction

∮E⋅dl=−dΦBdt\oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\Phi_B}{dt}

Third of Maxwell's equations showing that a time-varying magnetic flux induces an electric field.

maxwellfaradayinduction

Ampere-Maxwell Law

∮B⋅dl=μ0ic+μ0ϵ0dΦEdt\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 i_c + \mu_0 \epsilon_0 \frac{d\Phi_E}{dt}

Fourth of Maxwell's equations generalizing Ampere's law to include displacement current.

applies whenVacuum/free space.
maxwellampere

Momentum of EM Wave

p=Ucp = \frac{U}{c}

Momentum delivered to a surface by an EM wave transferring total energy U.

applies whenVacuum/free space.
momentumenergyjee-advanced

Photon Energy

E=hν=hcλE = h\nu = \frac{hc}{\lambda}

Energy of a discrete quantum (photon) of electromagnetic radiation.

applies whenQuantum description of EM waves.
photonenergyplanck

Poynting Vector

S=1μ0(E×B)\mathbf{S} = \frac{1}{\mu_0} (\mathbf{E} \times \mathbf{B})

Instantaneous rate of energy transfer per unit area.

applies whenVacuum/free space.
poynting_vectorenergy_flowjee-advanced

Direction of Wave Propagation

k^=E^×B^\hat{\mathbf{k}} = \hat{\mathbf{E}} \times \hat{\mathbf{B}}

Unit vector relation showing that the wave propagates in the direction of E cross B.

applies whenPlane electromagnetic wave.
propagationdirectioncross_productjee-advanced

Radiation Pressure (Absorbing Surface)

Pr=IcP_r = \frac{I}{c}

Pressure exerted by an electromagnetic wave on a perfectly absorbing surface.

applies whenPerfectly absorbing surface (normal incidence).
radiation_pressureabsorbingjee-advanced

Radiation Pressure (Reflecting Surface)

Pr=2IcP_r = \frac{2I}{c}

Pressure exerted by an electromagnetic wave on a perfectly reflecting surface.

applies whenPerfectly reflecting surface (normal incidence).
radiation_pressurereflectingjee-advanced

Speed of EM Waves in Vacuum

c=1μ0ϵ0c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}

The speed of light in free space based on absolute permeability and permittivity.

applies whenVacuum/free space.
speed_of_lightvacuum

Speed of EM Waves in a Medium

v=1μϵ=cμrϵrv = \frac{1}{\sqrt{\mu \epsilon}} = \frac{c}{\sqrt{\mu_r \epsilon_r}}

Wave speed inside a material medium with permeability μ and permittivity ε.

applies whenIsotropic dielectric/magnetic medium.
speed_mediumrefractive_index

Wave Speed Equation

c=νλ=ωkc = \nu\lambda = \frac{\omega}{k}

General kinematic relationship for the speed of the wave in terms of frequency and wavelength.

applies whenConstant wave speed.
speedfrequencywavelength

Total Current

i=ic+ϵ0dΦEdti = i_c + \epsilon_0 \frac{d\Phi_E}{dt}

The sum of conduction current and displacement current, which is continuous across a circuit.

currentcontinuity

Magnetic Field of an EM Wave

By=B0sin⁡(kz−ωt)=B0sin⁡[2π(zλ−tT)]B_y = B_0 \sin(kz - \omega t) = B_0 \sin\left[2\pi\left(\frac{z}{\lambda} - \frac{t}{T}\right)\right]

Equation for the transverse magnetic field component of a plane EM wave, in phase with the electric field.

applies whenPlane wave propagating in +z direction.
wave_equationmagnetic_field

Electric Field of an EM Wave

Ex=E0sin⁡(kz−ωt)=E0sin⁡[2π(zλ−tT)]E_x = E_0 \sin(kz - \omega t) = E_0 \sin\left[2\pi\left(\frac{z}{\lambda} - \frac{t}{T}\right)\right]

Equation for the transverse electric field component of a plane EM wave propagating in the +z direction.

applies whenPlane wave propagating in +z direction.
wave_equationelectric_field

Wave Vector Magnitude

k=2πλk = \frac{2\pi}{\lambda}

Relationship between the propagation constant (wave number) and wavelength.

wave_vectorwavelength
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