Advertisements
Advertisements
Question
Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is v = 50.0 MHz.
- Determine B0, ω, k, and λ.
- Find expressions for E and B.
Solution
Electric field amplitude, E0 = 120 N/C
Frequency of source, v = 50.0 MHz = 50 × 106 Hz
Speed of light, c = 3 × 108 m/s
(a) Magnitude of magnetic field strength is given as:
`"B"_0 = "E"_0/"c"`
= `120/(3 xx 10^8)`
= 4 × 10−7 T
= 400 nT
Angular frequency of the source is given as:
ω = 2πv
= 2π × 50 × 106
= 3.14 × 108 rad/s
Propagation constant is given as:
`"k" = ω/"c"`
= `(3.14 xx 10^8)/(3 xx 10^8)`
= 1.05 rad/m
Wavelength of the wave is given as:
`lambda = "c"/"v"`
= `(3 xx 10^8)/(50 xx 10^6)`
= 6.0 m
(b) Suppose the wave is propagating in the positive x-direction. Then, the electric field vector will be in the positive y-direction and the magnetic field vector will be in the positive z-direction. This is because all three vectors are mutually perpendicular.
Equation of the electric field vector is given as:
`vec("E") = "E"_0 sin ("k""x" - ω"t")hat"j"`
= `120 sin [1.05"x" - 3.14 xx 10^8"t"]hat"j"`
Magnetic field vector is given as:
`vec("B") = "B"_0 sin ("kx" - ω"t")hat"k"`
`vec("B") = (4 xx 10^-7) sin [1.05"x" - 3.14 xx 10^8"t"]hat"k"`
APPEARS IN
RELATED QUESTIONS
How are em waves produced by oscillating charges?
A charged particle oscillates about its mean equilibrium position with a frequency of 109 Hz. What is the frequency of the electromagnetic waves produced by the oscillator?
How is the speed of em-waves in vacuum determined by the electric and magnetic field?
Draw a sketch of linearly polarized em waves propagating in the Z-direction. Indicate the directions of the oscillating electric and magnetic fields.
What is the ratio of the speed of gamma rays to that of radio waves in a vacuum?
How are electric vector `(vec "E")`, magnetic vector `(vec "B")` and velocity vector `(vec "C")` oriented in an electromagnetic wave?
The energy contained in a small volume through which an electromagnetic wave is passing oscillates with
State any one property which is common to all electromagnetic waves.
How are electromagnetic waves produced? What is the source of the energy carried by a propagating electromagnetic wave?
Identify the electromagnetic radiations used
(i) In remote switches of a household electronic device; and
(ii) as a diagnostic tool in medicine
An e.m. wave is propagating in a medium with a velocity `vec"v" = "v" hat"i"`. The instantaneous oscillating electric field of this e.m. wave is along +y-axis, then the direction of an oscillating magnetic field of the e.m. wave will be along:
Write a short note on the radio waves.
A pulse of light of duration 10-6 s is absorbed completely by a small object initially at rest. If the power of the pulse is 60 x 10-3 W, calculate the final momentum of the object.
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.
The speed of plane electromagnetic waves is maximum in ______.
A man standing on the road has to hold his umbrella at 30° with the vertical to keep the rain away. He throws away the umbrella and starts, running at 10 km/h and finds raindrops hitting his head vertically. The speed of the raindrops with respect to the road is ______.
A plane electromagnetic wave travels in free space along x-axis. At a particular point in space, the electric field along y-axis is 9.3 Vm−1. The magnetic induction (B) along z-axis is:
A linearly polarized electromagnetic wave given as E = Eoî cos (kz – ωt) is incident normally on a perfectly reflecting infinite wall at z = a. Assuming that the material of the wall is optically inactive, the reflected wave will be given as ______.
Show that the radiation pressure exerted by an EM wave of intensity I on a surface kept in vacuum is I/c.
An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ∈ = 4.0. Then ______.
