# 24.2 Production of electromagnetic waves  (Page 3/14)

 Page 3 / 14

## Relating $E$ -field and $B$ -field strengths

There is a relationship between the $E$ - and $B$ -field strengths in an electromagnetic wave. This can be understood by again considering the antenna just described. The stronger the $E$ -field created by a separation of charge, the greater the current and, hence, the greater the $B$ -field created.

Since current is directly proportional to voltage (Ohm’s law) and voltage is directly proportional to $E$ -field strength, the two should be directly proportional. It can be shown that the magnitudes of the fields do have a constant ratio, equal to the speed of light. That is,

$\frac{E}{B}=c$

is the ratio of $E$ -field strength to $B$ -field strength in any electromagnetic wave. This is true at all times and at all locations in space. A simple and elegant result.

## Calculating $B$ -field strength in an electromagnetic wave

What is the maximum strength of the $B$ -field in an electromagnetic wave that has a maximum $E$ -field strength of $\text{1000 V/m}$ ?

Strategy

To find the $B$ -field strength, we rearrange the above equation to solve for $B$ , yielding

$B=\frac{E}{c}.$

Solution

We are given $E$ , and $c$ is the speed of light. Entering these into the expression for $B$ yields

$B=\frac{\text{1000 V/m}}{3\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}}=\text{3}\text{.}\text{33}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{T},$

Where T stands for Tesla, a measure of magnetic field strength.

Discussion

The $B$ -field strength is less than a tenth of the Earth’s admittedly weak magnetic field. This means that a relatively strong electric field of 1000 V/m is accompanied by a relatively weak magnetic field. Note that as this wave spreads out, say with distance from an antenna, its field strengths become progressively weaker.

The result of this example is consistent with the statement made in the module Maxwell’s Equations: Electromagnetic Waves Predicted and Observed that changing electric fields create relatively weak magnetic fields. They can be detected in electromagnetic waves, however, by taking advantage of the phenomenon of resonance, as Hertz did. A system with the same natural frequency as the electromagnetic wave can be made to oscillate. All radio and TV receivers use this principle to pick up and then amplify weak electromagnetic waves, while rejecting all others not at their resonant frequency.

## Take-home experiment: antennas

For your TV or radio at home, identify the antenna, and sketch its shape. If you don’t have cable, you might have an outdoor or indoor TV antenna. Estimate its size. If the TV signal is between 60 and 216 MHz for basic channels, then what is the wavelength of those EM waves?

Try tuning the radio and note the small range of frequencies at which a reasonable signal for that station is received. (This is easier with digital readout.) If you have a car with a radio and extendable antenna, note the quality of reception as the length of the antenna is changed.

## Phet explorations: radio waves and electromagnetic fields

Broadcast radio waves from KPhET. Wiggle the transmitter electron manually or have it oscillate automatically. Display the field as a curve or vectors. The strip chart shows the electron positions at the transmitter and at the receiver.

## Section summary

• Electromagnetic waves are created by oscillating charges (which radiate whenever accelerated) and have the same frequency as the oscillation.
• Since the electric and magnetic fields in most electromagnetic waves are perpendicular to the direction in which the wave moves, it is ordinarily a transverse wave.
• The strengths of the electric and magnetic parts of the wave are related by
$\frac{E}{B}=\text{c},$

which implies that the magnetic field $B$ is very weak relative to the electric field $E$ .

## Conceptual questions

The direction of the electric field shown in each part of [link] is that produced by the charge distribution in the wire. Justify the direction shown in each part, using the Coulomb force law and the definition of $\mathbf{E}=\mathbf{F}/q$ , where $q$ is a positive test charge.

Is the direction of the magnetic field shown in [link] (a) consistent with the right-hand rule for current (RHR-2) in the direction shown in the figure?

Why is the direction of the current shown in each part of [link] opposite to the electric field produced by the wire’s charge separation?

In which situation shown in [link] will the electromagnetic wave be more successful in inducing a current in the wire? Explain.

In which situation shown in [link] will the electromagnetic wave be more successful in inducing a current in the loop? Explain.

Should the straight wire antenna of a radio be vertical or horizontal to best receive radio waves broadcast by a vertical transmitter antenna? How should a loop antenna be aligned to best receive the signals? (Note that the direction of the loop that produces the best reception can be used to determine the location of the source. It is used for that purpose in tracking tagged animals in nature studies, for example.)

Under what conditions might wires in a DC circuit emit electromagnetic waves?

Give an example of interference of electromagnetic waves.

[link] shows the interference pattern of two radio antennas broadcasting the same signal. Explain how this is analogous to the interference pattern for sound produced by two speakers. Could this be used to make a directional antenna system that broadcasts preferentially in certain directions? Explain.

## Problems&Exercises

What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of $5\text{.}\text{00}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{T}$ (about 10 times the Earth’s)?

150 kV/m

The maximum magnetic field strength of an electromagnetic field is $5×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{T}$ . Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is $\text{0.75}c$ .

Verify the units obtained for magnetic field strength $B$ in [link] (using the equation $B=\frac{E}{c}$ ) are in fact teslas (T).

find the density of a fluid in which a hydrometer having a density of 0.750g/mL floats with 92.0% of its volume submerged.
Uniform speed
Sunday
(a)calculate the buoyant force on a 2.00-L Helium balloon.(b) given the mass of the rubber in the balloon is 1.50g. what is the vertical force on the balloon if it is let go? you can neglect the volume of the rubber.
To Long
Usman
Neshrin
a thick glass cup cracks when hot liquid is poured into it suddenly
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
Bala
what is the difference between atomic physics and momentum
find the dimensional equation of work,power,and moment of a force show work?
What's sup guys
Peter
cul and you all
Okeh
cool you bro
Nana
so what is going on here
Nana
hello peeps
Joseph
Michelson Morley experiment
how are you
Naveed
am good
Celine
you
Celine
hi
Bala
Hi
Ahmed
Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
OBERT
my project is Sol gel process how to prepare this process pls tell me
Bala
the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
Manyo
thanks jare
Doc
Thanks
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
what is physic
zalmia
Study of matter and energy
Fagbenro
physics is the science of matter and energy and their interactions
Acquah
physics is the technology behind air and matter
Doc
Okay
William
hi sir
Bala
how easy to understanding physics sir
Bala
Easy to learn
William