Wave Equation of EM Waves

Q.

A plane electromagnetic wave of wave intensity 6 $W/m^2$strikes a small mirror area 40 $c{m}^2$, held perpendicular to the approaching wave. The momentum transferred by the wave to the mirror each second will be

1. $6.4\times {10}^{-7}kg-m/s^2$

2. $4.8\times {10}^{-8}kg-m/s^2$

3. $3.2\times {10}^{-9}kg-m/s^2$

4. $1.6\times {10}^{-10}kg-m/s^2$

Q. In SI unit, the electric field of an E.M wave in free space is described by $E_y=400\sin \left[\pi \right({10}^{6}x-2ft\left)\right]$. Here, $f$ is the frequency.

1. Wave length of light is 2000 nm.
2. Frequency is $1.5\times {10}^{14}$ Hz.
3. This E.M wave is not visible for human eyes.
4. All of the above

Q.

The temperatures of two bodies A and B are ${727}^0$C and ${127}^0$ C. The ratio of rate of emission of radiations will be

1. 727/127

2. 625/16

3. 1000/400

4. 100/16

Q. An electromagnetic wave of frequency, $1\times {10}^4\text{Hz}$ is propagating along $z-$axis. The maximum amplitude of the electric field is $4\text{V/m}$. Average energy density of the electric field will be -

Q.

A wave is propagating in a medium of electric dielectric constant 2 and relative magnetic permeability 50. The wave impedance of such a medium is

1. 5 $\Omega$

2. 376.6 $\Omega$

3. 1883 $\Omega$

4. 3776 $\Omega$

Q. An electromagnetic wave of frequency $1\times {10}^{14}\text{Hz}$ is propagating along $Z-$axis. The amplitude of electric field is $4\text{V/m}$ . If $8.8\times {10}^{-12}{\text{C}}^2/\text{N}.{\text{m}}^2$ , then average energy density of electric field will be .

1. $35.2\times {10}^{-11}$ ${\text{J/m}}^3$
2. $35.2\times {10}^{-12}$ ${\text{J/m}}^3$
3. $35.2\times {10}^{-13}$ ${\text{J/m}}^3$
4. $35.2\times {10}^{-10}$ ${\text{J/m}}^3$

Q.

In an electromagnetic wave, the amplitude of electric field is 1 V/m. the frequency of wave is $5\times {10}^{14}$Hz. The wave is propagating along z-axis. The average energy density of electric field, in $Joule{m}^3$, will be

1. $1.1\times {10}^{-11}$

2. $2.2\times {10}^{-12}$

3. $3.3\times {10}^{-13}$

4. $4.4\times {10}^{-14}$

Q. An electromagnetic wave of frequency, $1\times {10}^4\text{Hz}$ is propagating along $z-$axis. The maximum amplitude of the electric field is $4\text{V/m}$. Average energy density of the electric field will be -

1. $35.4\times {10}^{-13}{\text{J/m}}^3$
2. $35.4\times {10}^{-11}{\text{J/m}}^3$
3. $35.4\times {10}^{-12}{\text{J/m}}^3$
4. $35.4\times {10}^{-10}{\text{J/m}}^3$

Q.

The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to $\frac{I}{8}$. The thickness of lead which will reduce the intensity to $\frac{l}{2}$ will be

1. 18 mm

2. 12 mm

3. 6 mm

4. 9 mm

Q.

A laser beam can be focussed on an area equal to the square of its wavelength. A He-Ne laser radiates energy at the rate of 1mW and its wavelength is 632.8 nm. The intensity of focussed beam will be

1. $1.5\times {10}^{13}W/m^2$

2. $2.5\times {10}^{9}W/m^2$

3. $3.5\times {10}^{17}W/m^2$

4. None of these

Q.

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 10m from the lamp will be

1. 1.34 V/m

2. 2.68 V/m

3. 5.36 V/m

4. 9.37 V/m

Q. Figure represents a capacitor made of two circular plates each of radius $r=12\text{cm}$ and separated by $d=5.0\text{mm}$. The capacitor is being charged by an external source. The charging current is constant current, $I=0.15\text{A}$.

Find the displacement current across the plates.

1. $1.5\text{A}$
2. $0.15\text{A}$
3. $0.015\text{A}$
4. $15\text{A}$

Q.

A radio receiver antenna that is 2 m long is oriented along the direction of the electromagnetic wave and receives a signal of intensity $5\times {10}^{-16}W/m^2$. The maximum instantaneous potential difference across the two ends of the antenna is

1. 1.23 mV

2. 1.23 mV

3. 1.23 V

4. 12.3 mV

Q. Suppose a wavefront originates from a point source as shown in the figure. Which of the following arrows correctly indicates the direction of propagation of light at point A?

1. $\downarrow$
2. $\uparrow$
3. $\to$
4. $\leftarrow$

Q.

Radiations of intensity $0.5W/m^2$ are striking a metal plate. The pressure on the plate is

1. $0.166\times {10}^{-8}N/m^2$

2. $0.332\times {10}^{-8}N/m^2$

3. $0.111\times {10}^{-8}N/m^2$

4. $0.083\times {10}^{-8}N/m^2$

Q.

In an electromagnetic wave, the amplitude of electric field is 1 V/m. the frequency of wave is $5\times {10}^{14}$Hz. The wave is propagating along z-axis. The average energy density of electric field, in $Joule{m}^3$, will be

1. $1.1\times {10}^{-11}$

2. $2.2\times {10}^{-12}$

3. $3.3\times {10}^{-13}$

4. $4.4\times {10}^{-14}$

Q. In an electromagnetic wave, the amplitude of electric field is $10{\text{Vm}}^{-1}$. The frequency of the wave is $5\times {10}^{14}\text{Hz}$ and the wave is propagating along $z–$axis, then total average energy density of E.M. wave is

1. $4.42\times {10}^{-10}{\text{Jm}}^{-3}$
2. $2.21\times {10}^{-10}{\text{Jm}}^{-3}$
3. $3.31\times {10}^{-10}{\text{Jm}}^{-3}$
4. $1.11\times {10}^{-10}{\text{Jm}}^{-3}$

Q. The electric field part of an electromagnetic wave in a medium is represented by
$E_x=0,$
$E_y=\left(2.5\frac{\text{N}}{\text{C}}\right)\cos [(2\pi \times {10}^6\text{rad/s})t-(\pi \times {10}^{-2}\text{rad/m})x],$
$E_z=0$.
The wave is :

1. Moving along $-x$ direction with frequency ${10}^6\text{Hz}$ and wavelength $200\text{m}$.
2. Moving along $+y$ direction with frequency $2\pi \times {10}^6\text{Hz}$ and wavelength $200\text{m}$.
3. Moving along $+x$ direction with frequency ${10}^6\text{Hz}$ and wavelength $100\text{m}$.
4. Moving along $+x$ direction with frequency ${10}^6\text{Hz}$ and wavelength $200\text{m}$.