Advertisements
Advertisements
Question
A laser beam has intensity 2.5 × 1014 W m−2. Find amplitudes of electric and magnetic fields in the beam.
Solution
Given:
Intensity, I = 2.5 × 1014 W/m2
We know :
`I = 1/2 ∈_0 E_0^2 c`
⇒ `E_0^2 = (2I)/(∈_0c)`
⇒ `E_0 = sqrt((2I)/(∈_0c))`
⇒ `E_0 = sqrt((2 xx 2.5 xx 10^14)/(8.85 xx 10^-12 xx 3 xx 10^8))`
⇒ `E_0 = 0.4339 xx 10^9`
⇒ `E_0 = 4.33 xx 10^8 "N/C"`
Maximum value of magnetic field ,
`B_0 = (E_0)/c`
`B_0 = (4.33 xx 10^8)/(3 xx 10^8)`
⇒ `B_0 = 1.43 "T"`
APPEARS IN
RELATED QUESTIONS
In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 1010 Hz and amplitude 48 V m−1.
- What is the wavelength of the wave?
- What is the amplitude of the oscillating magnetic field?
- Show that the average energy density of the E field equals the average energy density of the B field.
[c = 3 × 108 m s−1]
About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation
(a) at a distance of 1 m from the bulb?
(b) at a distance of 10 m?
Assume that the radiation is emitted isotropically and neglect reflection.
Arrange the following electromagnetic waves in order of increasing frequency:
ϒ-rays, microwaves, infrared rays and ultraviolet rays.
Speed of electromagnetic waves is the same
Consider the situation of the previous problem. Define displacement resistance Rd = V/idof the space between the plates, where V is the potential difference between the plates and id is the displacement current. Show that Rd varies with time as `R_d = R(e^(t"/"tau) - 1)` .
The energy levels of an atom of a certain element are shown in the given figure. Which one of the transitions A, B, C, D or E will result in the emission of photons of electromagnetic radiation of wavelength 618.75 nm? Support your answer with mathematical calculations.
Which of the following is false for electromagnetic waves.
The electric and magnetic fields, associated with an electromagnetic wave, propagating along negative X-axis can be represented by ______.
Which of the following is an electromagnetic wave?
What is displacement current?
Write down the integral form of modified Ampere’s circuital law.
Explain the Maxwell’s modification of Ampere’s circuital law.
Consider a parallel plate capacitor whose plates are closely spaced. Let R be the radius of the plates and the current in the wire connected to the plates is 5 A, calculate the displacement current through the surface passing between the plates by directly calculating the rate of change of flux of electric field through the surface.
Let an electromagnetic wave propagate along the x-direction, the magnetic field oscillates at a frequency of 1010 Hz and has an amplitude of 10-5 T, acting along the y – direction. Then, compute the wavelength of the wave. Also write down the expression for the electric field in this case.
In plane electromagnetic wave propagation velocity v, wavelength λ and frequency ν are related by ______.
The velocity of electromagnetic wave is parallel to
A plane electromagnetic wave propagating along x direction can have the following pairs of E and B.
- Ex, By.
- Ey, Bz.
- Bx, Ey.
- Ex, By.
An EM wave of intensity I falls on a surface kept in vacuum and exerts radiation pressure p on it. Which of the following are true?
- Radiation pressure is `I/c` if the wave is totally absorbed.
- Radiation pressure is `I/c` if the wave is totally reflected.
- Radiation pressure is `(2I)/c` if the wave is totally reflected.
- Radiation pressure is in the range `I/c < p < (2I)/c` for real surfaces.
A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm-1 along the y-direction. Its corresponding magnetic field component, B would be ______.
A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be x × 10-8 T. The value of x is ______.
