Class 12PhysicsElectromagnetic wavesMaxwell's equations , Concept of displacement current and Hertz experiment
EasyWrite Maxwell's equations.
(N/A) $(1)$ Gauss's law for electricity: $\oint \overrightarrow{E} \cdot d \overrightarrow{A} = \frac{Q}{\epsilon_{0}}$
$(2)$ Gauss's law for magnetism: $\oint \overrightarrow{B} \cdot d \overrightarrow{A} = 0$
$(3)$ Faraday's law: $\oint \overrightarrow{E} \cdot d \vec{l} = -\frac{d \Phi_{B}}{d t}$
$(4)$ Ampere-Maxwell law: $\oint \overrightarrow{B} \cdot d \vec{l} = \mu_{0} i_{c} + \mu_{0} \epsilon_{0} \frac{d \Phi_{E}}{d t}$
Where:
$\overrightarrow{E} = \text{electric field}$
$\overrightarrow{B} = \text{magnetic field}$
$d \overrightarrow{A} = \text{area element}$
$d \vec{l} = \text{line element}$
$\frac{d \Phi_{B}}{d t} = \text{rate of change of magnetic flux}$
$\frac{d \Phi_{E}}{d t} = \text{rate of change of electric flux}$
$i_{c} = \text{conduction current}$
$i_{d} = \epsilon_{0} \frac{d \Phi_{E}}{d t} = \text{displacement current}$
$\mu_{0} = \text{permeability of vacuum}$
$(2)$ Gauss's law for magnetism: $\oint \overrightarrow{B} \cdot d \overrightarrow{A} = 0$
$(3)$ Faraday's law: $\oint \overrightarrow{E} \cdot d \vec{l} = -\frac{d \Phi_{B}}{d t}$
$(4)$ Ampere-Maxwell law: $\oint \overrightarrow{B} \cdot d \vec{l} = \mu_{0} i_{c} + \mu_{0} \epsilon_{0} \frac{d \Phi_{E}}{d t}$
Where:
$\overrightarrow{E} = \text{electric field}$
$\overrightarrow{B} = \text{magnetic field}$
$d \overrightarrow{A} = \text{area element}$
$d \vec{l} = \text{line element}$
$\frac{d \Phi_{B}}{d t} = \text{rate of change of magnetic flux}$
$\frac{d \Phi_{E}}{d t} = \text{rate of change of electric flux}$
$i_{c} = \text{conduction current}$
$i_{d} = \epsilon_{0} \frac{d \Phi_{E}}{d t} = \text{displacement current}$
$\mu_{0} = \text{permeability of vacuum}$
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