# 24.1 Maxwell’s equations: electromagnetic waves predicted and  (Page 2/10)

 Page 2 / 10

Since changing electric fields create relatively weak magnetic fields, they could not be easily detected at the time of Maxwell’s hypothesis. Maxwell realized, however, that oscillating charges, like those in AC circuits, produce changing electric fields. He predicted that these changing fields would propagate from the source like waves generated on a lake by a jumping fish.

The waves predicted by Maxwell would consist of oscillating electric and magnetic fields—defined to be an electromagnetic wave (EM wave). Electromagnetic waves would be capable of exerting forces on charges great distances from their source, and they might thus be detectable. Maxwell calculated that electromagnetic waves would propagate at a speed given by the equation

$c=\frac{1}{\sqrt{{\mu }_{0}{\epsilon }_{0}}}.$

When the values for ${\mu }_{0}$ and ${\epsilon }_{0}$ are entered into the equation for $c$ , we find that

$c=\frac{1}{\sqrt{\left(8\text{.}\text{85}×{\text{10}}^{-\text{12}}\phantom{\rule{0.25em}{0ex}}\frac{{\text{C}}^{2}}{\text{N}\cdot {\text{m}}^{2}}\right)\left(4\pi ×{\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\frac{\text{T}\cdot \text{m}}{\text{A}}\right)}}=\text{3}\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s},$

which is the speed of light. In fact, Maxwell concluded that light is an electromagnetic wave having such wavelengths that it can be detected by the eye.

Other wavelengths should exist—it remained to be seen if they did. If so, Maxwell’s theory and remarkable predictions would be verified, the greatest triumph of physics since Newton. Experimental verification came within a few years, but not before Maxwell’s death.

## Hertz’s observations

The German physicist Heinrich Hertz (1857–1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. Starting in 1887, he performed a series of experiments that not only confirmed the existence of electromagnetic waves, but also verified that they travel at the speed of light.

Hertz used an AC $\text{RLC}$ (resistor-inductor-capacitor) circuit that resonates at a known frequency ${f}_{0}=\frac{1}{2\pi \sqrt{\text{LC}}}$ and connected it to a loop of wire as shown in [link] . High voltages induced across the gap in the loop produced sparks that were visible evidence of the current in the circuit and that helped generate electromagnetic waves.

Across the laboratory, Hertz had another loop attached to another $\text{RLC}$ circuit, which could be tuned (as the dial on a radio) to the same resonant frequency as the first and could, thus, be made to receive electromagnetic waves. This loop also had a gap across which sparks were generated, giving solid evidence that electromagnetic waves had been received.

Hertz also studied the reflection, refraction, and interference patterns of the electromagnetic waves he generated, verifying their wave character. He was able to determine wavelength from the interference patterns, and knowing their frequency, he could calculate the propagation speed using the equation $\upsilon =\mathrm{f\lambda }$ (velocity—or speed—equals frequency times wavelength). Hertz was thus able to prove that electromagnetic waves travel at the speed of light. The SI unit for frequency, the hertz ( $1 Hz=\text{1 cycle/sec}$ ), is named in his honor.

## Section summary

• Electromagnetic waves consist of oscillating electric and magnetic fields and propagate at the speed of light $c$ . They were predicted by Maxwell, who also showed that
$c=\frac{1}{\sqrt{{\mu }_{0}{\epsilon }_{0}}},$

where ${\mu }_{0}$ is the permeability of free space and ${\epsilon }_{0}$ is the permittivity of free space.

• Maxwell’s prediction of electromagnetic waves resulted from his formulation of a complete and symmetric theory of electricity and magnetism, known as Maxwell’s equations.
• These four equations are paraphrased in this text, rather than presented numerically, and encompass the major laws of electricity and magnetism. First is Gauss’s law for electricity, second is Gauss’s law for magnetism, third is Faraday’s law of induction, including Lenz’s law, and fourth is Ampere’s law in a symmetric formulation that adds another source of magnetism—changing electric fields.

## Problems&Exercises

Verify that the correct value for the speed of light $c$ is obtained when numerical values for the permeability and permittivity of free space ( ${\mu }_{0}$ and ${\epsilon }_{0}$ ) are entered into the equation $c=\frac{1}{\sqrt{{\mu }_{0}{\epsilon }_{0}}}$ .

Show that, when SI units for ${\mu }_{0}$ and ${\epsilon }_{0}$ are entered, the units given by the right-hand side of the equation in the problem above are m/s.

#### Questions & Answers

what is Andromeda
what is velocity
displacement per unit time
Murlidhar
the ratec of displacement over time
Jamie
the rate of displacement over time
Jamie
the rate of displacement over time
Jamie
did you need it right now
Pathani
up to tomorrow
Santosh
i need a description and derivation of kinetic theory of gas
Santosh
pls the sum of change in kinetic and potential energy is always what ?
Faith
i need a description and derivation of kinetic theory of gas
Santosh
did you need it right now
Pathani
A few grains of table salt were put in a cup of cold water kept at constant temperature and left undisturbed. eventually all the water tasted salty. this is due to?
Aunt Faith,please i am thinking the dissolution here from the word "solution" exposed the grains of salt to be dissolved in the water.Thankyou
Junior
Junior
Aunt Faith,please i am thinking the dissolution here from the word "solution" exposed the grains of salt to be dissolved in the water.Thankyou
Junior
it is either diffusion or osmosis. just confused
Faith
due to solvation....
Pathani
what is solvation pls
Faith
water molecule surround the salt molecules . solute solute attraction break in the same manner solvent solvent interaction also break. as a result solute and solvent attraction took place.
Pathani
okay thanks
Faith
my pleasure
Pathani
what is solvation pls
Faith
water act as a solvent and salt act as solute
Pathani
okay thanks
Faith
its ok
Pathani
due to solvation....
Pathani
water molecule surround the salt molecules . solute solute attraction break in the same manner solvent solvent interaction also break. as a result solute and solvent attraction took place.
Pathani
what is magnetism
physical phenomena arising from force caused by magnets
is the phenomenon of attracting magnetic substance like iron, cobalt etc.
Faith
what is heat
Heat is a form of energy where molecules move
saran
topic-- question
Salman
I know this is unrelated to physics, but how do I get the MCQs and essay to work. they arent clickable.
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
why is a body moving at a constant speed able to accelerate
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian
because it changes only direction and the speed is kept constant
Justice
Why is the sky blue...?
It's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic
Mike
A heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel
A thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to
Be raised until its distance from d lens is 27cm find d radius of curvature
Azummiri
what happens when a nuclear bomb and atom bomb bomb explode add the same time near each other
A monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question
v2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.
Ramonyai
why is the north side is always referring to n side of magnetic