Electromagnetic Waves - Important Formulas Table

 

Electromagnetic Waves - Important Formulas Table

S.No.	Concept / Quantity	Formula	Key Notes
1	Speed of Electromagnetic Wave in Vacuum	$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8$ m/s	Fundamental relation
2	Speed of EM Wave in Medium	$v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{c}{\sqrt{\mu_r \epsilon_r}}$	$\mu_r \epsilon_r = n^2$
3	Relation between E and B	$E_0 = c B_0$ or $E = c B$	In vacuum
4	Magnetic Field due to Displacement Current	$B = \frac{\mu_0 I_d}{2\pi r}$	Maxwell’s correction
5	Displacement Current	$I_d = \epsilon_0 \frac{d\phi_E}{dt}$	-
6	Total Current (Conduction + Displacement)	$I_{\text{total}} = I_c + I_d$	Continuity in Maxwell’s equations
7	Poynting Vector (Energy Flux)	$\vec{S} = \frac{1}{\mu_0} \vec{E} \times \vec{B}$	Direction of energy flow
8	Average Intensity of EM Wave	$I = \frac{1}{2} c \epsilon_0 E_0^2 = \frac{E_0 B_0}{2\mu_0}$	Time-averaged
9	Momentum of EM Wave	$p = \frac{U}{c}$ (for complete absorption)	Radiation pressure
10	Radiation Pressure (Complete Absorption)	$P = \frac{I}{c}$	-
11	Radiation Pressure (Complete Reflection)	$P = \frac{2I}{c}$	-
12	Energy Density in Electric Field	$u_E = \frac{1}{2} \epsilon_0 E^2$	-
13	Energy Density in Magnetic Field	$u_B = \frac{B^2}{2\mu_0}$	-
14	Total Average Energy Density	$u_{avg} = \frac{1}{2} \epsilon_0 E_0^2$	$u_E = u_B$
15	Wavelength-Frequency Relation	$c = \nu \lambda$	In vacuum
16	Refractive Index	$n = \sqrt{\mu_r \epsilon_r} = \frac{c}{v}$	-
17	Intensity in terms of RMS Electric Field	$I = \frac{1}{2} c \epsilon_0 E_{rms}^2$	$E_{rms} = \frac{E_0}{\sqrt{2}}$
18	Wave Number	$k = \frac{2\pi}{\lambda}$	-
19	Angular Frequency	$\omega = 2\pi \nu = ck$	-
20	EM Wave Equation (Electric Field)	$\frac{\partial^2 E}{\partial x^2} = \mu_0 \epsilon_0 \frac{\partial^2 E}{\partial t^2}$	-

Important Constants

• $\mu_0 = 4\pi \times 10^{-7}$ T m/A
• $\epsilon_0 = 8.85 \times 10^{-12}$ C²/N m²
• Speed of light $c = 3 \times 10^8$ m/s
• $\frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8$ m/s (exact)

Note: This chapter is theoretical and conceptual. All formulas are in SI units. These are most important for Class 12 Board Examinations, JEE Main, NEET, and JEE Advanced.