Maxwell's Equations and Electromagnetic Waves - Class XI

Given: The frequency of the electromagnetic wave is $25\ MHz$.

To find: The quantity that is independent of the wavelength.

Maxwell's equations are:

The emitted X-rays transfer energy to the material on which it is falling.

Displacement current Id = epsilon_0 * (dPhi_E / dt). Phi_E = E * A = (V/d) * A. Id = epsilon_0 * A * (1/d) * (dV/dt). Given V=400, d=2mm=210^-3m, A=60cm^2=6010^-4m^2, dt=10^-6s. Assuming dV=400V, Id = (8.85410^-12 * 6010^-4 * 400) / (2*10^-3 * 10^-6) = 2.125 * 10^-2 A. The result is approximately 2.062 * 10^-2 A.

According to Maxwell's hypothesis, a displacement current will flow through a capacitor when the potential difference across its plates is varying. Thus a varying electric field will exist between the plates and this displacement current is same in magnitude to the current flowing in outer circuit.  When a D.C voltage applied across its plates, constant voltage appears across its plates and so there will be no displacement current flowing through the capacitor. Thus the displacement current will flow when the potential is increasing with time.

In electromagnetism, displacement current is a quantity appearing in Maxwell's equations that is defined in terms of the rate of change of electric displacement field.

Velocity of light in a medium,

$\displaystyle c=\frac{1}{\sqrt{\mu _0\varepsilon _o\mu _r\varepsilon _r}}=\frac{1}{\sqrt{\mu\varepsilon}}$

Maxwell's equation describe the fundamental laws of electricity and magnetism. His equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.

The speed of light in a medium is given by v = f * lambda. Since frequency (f) remains constant when light moves between media, the wavelength (lambda) is directly proportional to the speed of light (v) in that medium.

The given equation is Ampere-Maxwell law, which modifies Ampere's original circuital law by adding the displacement current term proportional to the rate of change of electric flux. This completes the set of Maxwell's equations for electromagnetism.

Light consists of electric and magnetic field that are perpendicular ${ 90 }^{ 0 }$ to each other.
APPOACH by example
Electric field inside plates. The magnetic field this given rise to via the displacement current is along the perimeter of the circle parallel to capauatates plates.

Flux of certain closed surface is zero and so it tells that net magnetic charge is equal to zero. This is possible when there are two equal and opposite poles.

1. Photoelectric effect was discovered by heinrich Rudoy Hertz.
2. Compton effect was discovered by Aethur Holl Compton.
3. Raman effect was discovered by Sir Chandrasekhar Venbata Ram. 

The displacement current in a charging capacitor is equal to the conduction current in the circuit. The current in an RC circuit is I(t) = (epsilon/R) * e^(-t/RC). Since the surface area A/2 is parallel to the plates, it intercepts half the electric flux, leading to a factor of 1/2.

According to Maxwell's hypothesis, changing of electric field gives rise to Magnetic field.

Given,
$I=\dfrac { { I } _{ 0 } }{ 2 } $              ....(i)
${ I }^{ ' }=I\cos ^{ 2 }{ \theta  } $                 $\left( \because { I }^{ ' }=\dfrac { { I } _{ 0 } }{ 8 }  \right) $
$\therefore \dfrac { { I } _{ 0 } }{ 8 } =\dfrac { { I } _{ 0 } }{ 2 } \cos ^{ 2 }{ \theta  } $
From the equation (i), we have
$\dfrac { 1 }{ 4 } =\cos ^{ 2 }{ \theta  } \Rightarrow \cos { \theta  } ={ 1 }/{ 2 }$
$\Rightarrow \cos { \theta  } =\cos { { 60 }^{ o } } $
$\Rightarrow \theta ={ 60 }^{ o }$