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Showing posts with the label Electromagnetic Wave Theory

### Physical Significance of Maxwell's Equations

Physical Significance: The physical significance of Maxwell's equations obtained from integral form are given below: Maxwell's First Equation: 1. The total electric displacement through the surface enclosing a volume is equal to the total charge within the volume. 2. It represents Gauss Law. 3. This law is independent of time. Charge acts as source or sink for the lines of electric force. Maxwell's Second Equation: 1. The total magnetic flux emitting through any closed surface is zero. An isolated magnet do not exist monopoles. 2. There is no source or sink for lines of magnetic force. 3. This is time independent equation. Maxwell's Third Equation: 1. The electromotive force around the closed path is equal to the time derivative of the magnetic displacement through any surface bounded by the path. 2. This gives relation between electric field $E$ and magnetic induction $B$. 3. This expression is time varying i.e. $E$ is generate

### Characteristics of Electromagnetic Wave

Electromagnetic Wave: An electromagnetic wave is the combined effect of an electric field and magnetic field which carry energy from one place to another. When an electric field and the magnetic field are applied perpendicular to each other then a wave propagates perpendicular to both the electric field and the magnetic field. This wave is called the electromagnetic wave. Characteristics of Electromagnetic Wave: 1.) Electric and Magnetic Fields: Electromagnetic waves are produced through the mutually perpendicular interaction of electric and magnetic fields. The propagation of the wave is also perpendicular to both the electric field and the magnetic field. 2.) Wave Nature of electromagnetic waves: Electromagnetic waves are characterized by their wave-like behavior, so they exhibit the properties such as wavelength, frequency, amplitude, and velocity. This wave-like behavior of electromagnetic waves can undergo phenomena like interference, diffraction, and polarization. 3.

### Poynting Vector and Poynting Theorem

Poynting Vector: The rate of flow of energy per unit area in plane electromagnetic wave is known as Poynting vector. It is represented by $\overrightarrow{S}$. It is a vector quantity. $\overrightarrow{S}=\overrightarrow{E} \times \overrightarrow{H}$ $\overrightarrow{S}=\frac{1} {\mu_{0}} (\overrightarrow{E} \times \overrightarrow{B})$ Poynting Theorem (Work energy theorem): The most important aspect of electrodynamics is: Energy density stored with an electromagnetic wave Energy Flux associated with an electromagnetic wave To derive the energy density and energy flux. We consider the conservation of energy in small volume elements in space. The work done per unit volume by an electromagnetic wave: $W=\overrightarrow{J}.\overrightarrow{E} \qquad(1)$ This work done also consider as energy dissipation per unit volume. This energy dissipation must be connected with the net decrease in energy density and energy flow out of the volume.

### Derivation of Maxwell's forth equation

Maxwell's fourth equation is the differential form of Ampere's circuital law. $\overrightarrow{\nabla} \times \overrightarrow{H} = \overrightarrow{J} + \frac{\partial{\overrightarrow{D}}}{\partial{t}}$ Derivation: According to Ampere's circuital law $\oint_{l} \overrightarrow{B}. \overrightarrow{dl}=\mu_{0} i \qquad(1)$ According to Stroke's theorem- $\oint_{l} \overrightarrow{B}.\overrightarrow{dl}=\oint_{S} (\overrightarrow{\nabla} \times \overrightarrow{B}). \overrightarrow{dS} \qquad(2)$ From equation$(1)$ and equation$(2)$ $\oint_{S} (\overrightarrow{\nabla} \times \overrightarrow{B}). \overrightarrow{dS} = \mu_{0} i \qquad(3)$ where $i=\oint_{S} \overrightarrow{J}. \overrightarrow{dS} \qquad(4)$ So from equation$(3)$ and equation$(4)$ $\oint_{S} (\overrightarrow{\nabla} \times \overrightarrow{B}). \overrightarrow{dS} = \mu_{0} \oint_{S} \overrightarrow{J}. \overrightarrow{dS}$ \$\oint_{S} (\over