Electromagnetic waves are a result of vibrations between an electric field and a magnetic field. In other words, Electromagnetic waves are composed of oscillating magnetic and electric fields. In this article, we will see some important electromagnetic wave formulas which will also help you in preparation for competitive exams like JEE and NEET.
Index
Maxwell’s equations
\( \oint E \cdot dA=Q/\varepsilon _{0}\; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\)(Gauss’s Law for electricity)
\( \oint B \cdot dA=0 \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\)(Gauss’s Law for magnetism)
\( \oint E \cdot d\iota =\frac{-d\phi B}{dt} \; \; \; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \)(Faraday’s Law)
\(\oint B \cdot dl= \mu_{0}i_{c} + \mu_{0} \epsilon_{0}\frac{d\phi_{E}}{dt}\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\; \)(Ampere-Maxwell Law)
Oscillating Electric and Magnetic fields
\( E=E_{x}(t)=E_{0}\; sin\; (KZ-\varpi t) \) \( = E_{0}\; sin\; \left [ 2\pi \left ( \frac{z}{\lambda }-vt \right ) \right ]=E_{0}\; sin\left [ 2\pi \left ( \frac{z}{\lambda }-\frac{t}{T} \right ) \right ]\; \; E_{0}/B_{0}=c \)\(c=1\sqrt{ \mu_{0} \epsilon_{0} }\; \; \; \; \), c is speed of light in vaccum
\( v=1/\sqrt{\mu \epsilon }\; \; \; \;\), v is speed of light in medium
\( p=\frac{U}{c}\), energy transferred to a surface in time t is U, the magnitude of the total momentum delivered to this surface (for complete absorption) is p
Electromagnetic Spectrum
| Type | Wavelength range | Production | Detection |
| Radio | \(> 0.1m\) | Rapid acceleration and decelerations of electrons in aerials | Receiver’s aerials |
| Microwave | 0.1m to 1mm | Klystron value or magnetron value | Point contact diodes |
| Infra-red | 1mm to 700nm | The vibration of atoms and molecules | Thermopiles Bolometer, Infrared photographic film |
| Light | 700nm to 400nm | Electrons in atoms emit light when they move from one energy level to a lower energy | The eye, photocells, Photographic film |
| Ultraviolet | 400nm to 1nm | Inner shell electrons in atoms moving from one energy level to a lower level | photocells photographic film |
| X-rays | \( 1nm\; to\; 10^{-3}nm \) | X-ray tubes or inner shell electrons | Photograpic film, Geiger tubes, lonisation chamber |
| Gamma rays | \( < 10^{-3}nm\) | Radioactive decay of the nucleus | do |
