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  • Restate Maxwell’s equations.

The Scotsman James Clerk Maxwell (1831–1879) is regarded as the greatest theoretical physicist of the 19th century. (See [link] .) Although he died young, Maxwell not only formulated a complete electromagnetic theory, represented by Maxwell’s equations    , he also developed the kinetic theory of gases and made significant contributions to the understanding of color vision and the nature of Saturn’s rings.

This black and white engraving shows physicist James Clerk Maxwell as a Victorian era gentleman dressed in bowtie, vest, and jacket, and sporting a full, graying beard and moustache.
James Clerk Maxwell, a 19th-century physicist, developed a theory that explained the relationship between electricity and magnetism and correctly predicted that visible light is caused by electromagnetic waves. (credit: G. J. Stodart)

Maxwell brought together all the work that had been done by brilliant physicists such as Oersted, Coulomb, Gauss, and Faraday, and added his own insights to develop the overarching theory of electromagnetism. The results of Maxwell’s equations are paraphrased here in words because their mathematical statement is beyond the level of this text. However, the equations illustrate how apparently simple mathematical statements can elegantly unite and express a multitude of concepts—why mathematics is the language of science.

The results of maxwell’s equations

  1. Electric field lines originate on positive charges and terminate on negative charges. The electric field is defined as the force per unit charge on a test charge.
  2. Magnetic field lines are continuous, having no beginning or end. No magnetic monopoles are known to exist.
  3. A changing magnetic field induces an electric field.
  4. Magnetic fields are generated by moving charges or by changing electric fields.

Maxwell’s equations encompass the major laws of electricity and magnetism. What is not so apparent is the symmetry that Maxwell introduced in his mathematical framework. Especially important is his addition of the hypothesis that changing electric fields create magnetic fields. This is exactly analogous (and symmetric) to Faraday’s law of induction and had been suspected for some time, but fits beautifully into Maxwell’s equations.

Making connections: unification of forces

Maxwell’s complete and symmetric theory showed that electric and magnetic forces are not separate, but different manifestations of the same thing—the electromagnetic force. This classical unification of forces is one motivation for current attempts to unify the four basic forces in nature—the gravitational, electrical, strong, and weak nuclear forces.

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 the speed of light,

c = 3.00 × 10 8 m / s .

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 circuit that resonates at a known frequency 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 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.

The circuit diagram shows a simple circuit containing an alternating voltage source, a resistor R, capacitor C and a transformer, which provides the impedance. The transformer is shown to consist of two coils separated by a core. In parallel with the transformer is connected a wire loop labeled as Loop one Transmitter with a small gap that creates sparks across the gap. The sparks create electromagnetic waves, which are transmitted through the air to a similar loop next to it labeled as Loop two Receiver. These waves induce sparks in Loop two, and are detected by the tuner shown as a rectangular box connected to it.
The apparatus used by Hertz in 1887 to generate and detect electromagnetic waves. An AC circuit connected to the first loop caused sparks across a gap in the wire loop and generated electromagnetic waves. Sparks across a gap in the second loop located across the laboratory gave evidence that the 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 υ = size 12{υ=fλ} {} (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 = 1 cycle/sec size 12{1" Hz"=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
  • 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.

Questions & Answers

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Simran Reply
what do you mean 'mri'
Nimco
short for magnetic resonance imaging. "the researchers used MRI to record the brain activity" a medical examination performed using magnetic resonance imaging. "he's having an MRI to determine the extent of the injury" an image obtained by magnetic resonance imaging. "after looking at the MRI, the d
Riyaz
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Ibrahim Reply
i do not know
Nimo
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Japhar
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Nimco
Sutures are immovable junction between two bones e.g those of the skull
Surphy
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Japhar
Between the heart and the Brain which one is more important to human being... discuss
Faith Reply
well the brain is important for motor skills, the heart is important for involuntary muscle movement supporting body functions. the body can survive without brain involvement, but the body cannot last without the heart
john
granted the heart is important, but the brain gives the body purpose
john
the brain is more important
Kevin
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john
brain
tracey
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Dzifa
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john
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Kevin
heart
Kevin
it is difficult to select which organ is more important, now you can replace the heart with a mechanical device and the body could still function, and with technology today brain activity can also be replicated. But life would not be the same
john
there's coordination btn the two..so without any of them no life
Japhar
the heart
The brain is important to humans.
Zozo
what is homeostasis
Rebecca Reply
It is the condition when body feel comfortable
Jazil
Wo feels hungry, thirty due to homeostasis
Jazil
Is the maintenance of the internal environment of all the body cells for normal growth
Komolika
what is the composition of saliva
Vijay Reply
ഫസ്റ്റ് ചാപ്റ്റർ ഇംപോർട്ടൻസ് പോസ്റ്റ്
Reshma Reply
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Loving
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Anshika
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Loving
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Loving
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Asad
I don't know but would like to
Rebecca
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Ifunanya Reply
patellar
Ibrahim
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Michael Reply
cell is the structural and functional unit of living organisms
Fidel
Which of the following hormones are responsible for the adolescent growth spurt? estrogen and testosterone, even in women?
Kepa Reply
estrogen
Farhana
Estrogen!
Jazil
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Michael
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Anshika
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testrogen
Rebecca
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adamu Reply
a sling a rope used in hunting ie throwing of rocks
Michael
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Arman Reply
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adamu
joint have 3 cartilaginous joint fibrous joint synovial joint U can reserch in Google can explain U well
sopheaktra
define sling
adamu
To throw with a circular or arcing motion
real
pls hux I was given an assignment,, Between the heart and Brain which one is more important to human being... discuss
Faith
what is respiration
Osele Reply
what is respiration
Paul
Respiration is the process by which oxygen is taken in and carbon dioxide is given out.
Md
Respiration is the combination of inhalation and exhalation.
Khim
inhalation is the taking in air from environment to lung and exhalation is taking out sir from the lung to environment ..
Khim
is the process by wich gases(oxygen and carbon(IV)oxide go through the nose, trachea and the lungs to the blood stream
Michael
what is holistic
Kibrom Reply
Holistic means encompassing the whole of a thing, and not just the part. Holistic medicine looks at the whole person for answers, not just at physical symptoms. You might have heard of holistic medicine, which tries to treat someone as mind and body, instead of treating only the part of the patient
I want to learn one by one system like skeleton system... muscular system
Mary Reply
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Kibrom
what is the difference between regional anatomy and system anatomy
David
system anatomy is when we study the system like digestive, circulatory, reproductive, but regional anatomy is studying the anatomy by regions of body like anatomy of neck, thorax, head etc. Regional anatomy may include system anatomy...
Biplav
yes
Anshika
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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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