Introduction to electromagnetic waves - class-XII

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 } } $
$\Rightarrow \theta ={ 60 }^{ o }$

All electromagnetic waves (EM waves) travel with the speed of light in vacuum but these have different frequency, amplitude, wavelength and intensity.

Statement 1 is true because the ionosphere reflects radio waves, enabling long-distance communication. Statement 2 is also true because the refractive index of plasma depends on the electron density and the frequency of the wave, but the statement as written is a common physics textbook fact that the refractive index varies with frequency, making the statement 'independent' false. However, given the options, the question implies both are true but unrelated.

Infrasonic waves are mechanical waves that require a medium (like air, water, or solids) to propagate; therefore, they cannot travel through a vacuum.

Light can pass through vacuum,glass and air.

Answer A is correct 

Electromagnetic wave does not require any material medium to propagate. These can also travel through vacuum. Also EM waves travel with the speed equal to that of light  i.e $3 \times 10^8$ m/s

EM waves do not require a material medium to travel, these can propagate even through vacuum while all other waves require a certain medium to travel.

UV waves are shorter than visible light waves, so UV possesses more energy than regular light.

UV photons have the right energies to cause chemical changes. When UV light hits your skin, the DNA in your skin cells can undergo chemical change. This chemical change is what sunburn is. In extreme cases, this change in DNA can result in cancer.

The electric and magnetic field components of a linearly polarized electromagnetic wave oscillate in such a way that they peak at the same time and they become zero at the same time but they point to different directions in space, separated by an angle of $90^{\circ}$.

EM waves are formed by electric and magnetic fields but are not deflected by them, and also they can be deflected by gravitational field....

 Light (electromagnetic wave) has an electric and a magnetic field and should thus deflect a compass needle during daytime.

Visible light - Being an Electromagnetic wave is reflected by glass (take mirror).

For highly intense X-Rays & gamma rays, take that the mirror is stronger such that it could resist for at least 30 seconds.

hence, light wave neither electric field nor magnetic field

The de Broglie wavelength of an electron is given by lambda = h / p = h / sqrt(2 m E). Substituting the energy of 10 keV and the mass and charge constants yields approximately 0.12 Angstroms.

In an electromagnetic wave, electrical and magnetic fields are perpendicular to each other. The wave propagates in a direction perpendicular to both electric and magnetic fields as given by  $\vec E\times \vec B$.

Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. This perpendicular oscillation makes them strictly transverse in nature.

Answer is B.

Infrared (IR) is invisible radiant energy, electromagnetic radiation with longer wavelengths than those of visible light, extending from the nominal red edge of the visible spectrum at 700 nano-meters to 1 mm. 
Infrared is used in night vision equipment when there is insufficient visible light to see. Night vision devices operate through a process involving the conversion of visible light photons into electrons that are then amplified by a chemical and electrical process and then converted back into visible light. Infrared light sources can be used to enhance the available visible light for conversion by night vision devices, increasing in-the-dark visibility without actually using a visible light source.

Light appears to travel in a straight line because diffraction (or deviation from the path) is least in light. Diffraction is least because -of small wavelength of light. So small wave length of light causes the light to travel almost in straight line.

Gamma rays have the highest frequency.

The speed at which the light travels in vacuum is $3×10^8m/s$

In vacuum, electromagnetic waves travel at speed of $3\times { 10 }^{ 8 }$ m/s.

Reflection of light wave at fixed point result in phase difference b/w incident and reflected ray of $\pi$. The wave gets inverted. Inversion behavior is noticed when medium is connected to dense medium.

A. Both magnetic and electric field.

In electromagnetic waves,

$\vec{E} = E _0 \left(\dfrac{i + j}{\sqrt{2}}\right) \cos (kz + wt)$