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---------------------- 2310 - Getting Light from Electricity and Magnetism
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- In 1785 Charles Coulomb and Henry Cavendish developed the formula for the force between two electric charges. The electric force is directly proportional to the product of the two electric charges and inversely proportional to the square of the distance between them.
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--------------------------- Electric Force = Constant * q1 * q2 / r^2
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- Where q1 and q2 are the strengths of the electric charges in coulombs. “r” is the distance between them in meters. The Constant is the constant of proportionality for electric charges, “kC”.
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- Strangely enough this is very similar to the formula for the force of gravity:
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--------------------------- Gravity Force = G * M1 * m2 / r^2
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- The force of gravity is directly proportional to the two masses, in kilograms, and inversely proportional to the square of the distance between them in meters.
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- G is the gravitational constant of proportionality. It is constant number that depends on the units of measurement. In this case the force is in newtons, the distance in meters and the mass in kilograms. The constant number is determined in the laboratory with known conditions and precise measurements:
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----------------------------- G = 6.7 * 10^-11 newton * meters^2 / kilograms^2
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- “kC” is the constant of electric charge, called Coulomb’s constant:
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---------------------------- kC = + or - 9 * 10^9 newton * meter^2 / coulomb^2
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---------------------------- kC = + or - 9 * 10^-12 farads / meter, using different units of measurement
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- The gravitational force is always positive, but the electric force can be positive or negative, depending on the charges where unlike charges attract or like charges repel.
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- The electric force is enormously stronger than the gravitational force. The attractive force between an electron and a proton is 10^38 times stronger than the gravitational force.
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- Constants of proportionality are numbers determined in the laboratory using known conditions and precise measurements
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- The gravitational constant = G = 6.669 * 10^-11 newton * meters^2 / kilograms^2
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- The constant of electric charge = kC = 8.8554187817 * 10^-12 farads / meter
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----------------------------- The gravitational force between a proton and an electron is:
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----------------------------- F = G * mass of proton * mass of electron / radius^2
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----------------------------- F = 6.669 * 10^-11 * 1.167252*10^-27 * 9.1091 * 10^-31 / 10^-20
----------------------------- F = 7.09 * 10^-48
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----------------------------- The electric force between a proton and an electron is:
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----------------------------- F = kc * charge of proton * charge of electron / radius^2
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----------------------------- F = 8.854 * 10^-12 * 1.6 *10^-19 / 10^-20
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----------------------------- F = 2.3 * 10^-10
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- The force of electric charge is 10^38 times stronger than the force of gravity.
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- The huge size of the electric force is evidence that the total charge in the universe must be zero. Otherwise there would be massive collisions happening everywhere.
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- Your body is electrically neutral while it contains 10^29 electrons and protons. If even one out of 10,000 electrons somehow migrated to the center of the Earth you would be smashed by a coulomb force one million times the force of gravity. It is a good thing to stay electrically neutral.
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- In 1820 Hans Christian Oersted of Denmark ( See footnote 1 ) found that a wire carrying electric current deflected a nearby compass needle. Andre-Marie Ampere quantified Hans’ observation. Ampere determined how much magnetic field is produced by a given amount of electric current. His formula states that the magnetic field at a given point in space is proportional to the current and inversely proportional to the distance from the wire.
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-------------------------------- Strength of the Magnetic Field, B = Constant * I / r
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-------------------------------- I = the electric current in amperes
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--------------------------------- r = the distance in meters
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-------------------------------- B = The constant of proportionality for magnetic force
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- A moving charge, or current, produces a magnetic field. So, can a moving magnetic field produce a current?
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- Yes, in 1829 Michael Faraday and Joseph Henry (See footnote 2) both demonstrated that a coil of wire with a magnet moving in and out would induce an alternating current in the wire. The current stops when the magnetic stops moving.
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- Faraday’s formula for a changing magnetic field producing an electric current is:
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---------------------------------- I = Constant * change in B / change in time
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- Current is dependent on the rate of change of the magnetic field. And, the force of the magnetic field is always at right angles to the direction of the current.
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- So, electric force, magnetic force, and gravity force are very similar. Some differences are that gravity forces are always positive, electric forces can be positive or negative, and magnetic forces are always at right angles to the direction of motion.
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- At a given point in space gravity is pulling a certain mass, m, with a force, F. The field strength at that point is defined as:
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---------------------------------- g = F / m
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---------------------------------- Gravity acceleration = Force / mass
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- “g” is the acceleration of gravity. This comes from the equation, force = mass * acceleration. At the surface of the Earth gravity acceleration is:
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--------------------------------- g = 9.8 meters / seconds^2.
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- We can calculate the acceleration of gravity using the mass of the Earth, the radius of the Earth, and the gravitational constant.
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-------------------------------- F = G * M * m / r^2
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------------------------------- F = m * a = or in this case, m * g
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------------------------------- g = G * M / r^2
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------------------------------- g = 6.67 * 10^-11 * 5.9742 * 10^24 / (6.378 * 10^6 )^2
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------------------------------- g = 9.796 meters / sec^2
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- The electric field is similar. At a given point in space the electric force, F, is pulling or pushing a certain electric charge, “q”
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-------------------------------- E = F / q
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-------------------------------- Electric Field Strength = Force / Coulombs of electric charge
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------------------------------- Electric Field Strength, E = Newtons / Coulomb
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- Electric currents are electric charges in motion. And, a moving charge produces a magnetic field.
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----------------------------- Magnetic Field Strength, B = Constant * E / r
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- This formula says that an electric field produces a magnetic field.
Where kB is the constant of proportionality for magnetic force.
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----------------------------- kB = 1.26 * 10^-6 henrys / meter
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---------------------------- E = Constant * change in B / change in time
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- This formula says a changing magnetic field produces an electric field.
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- James Clerk Maxwell in 1864 thought that due to symmetry alone a logical conclusion would be that a changing electric field could produce a magnetic field. He developed several equations to define this condition and concluded that it was impossible to consider an electric field or a magnetic field in isolation. They are intertwined.
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- A changing electric field induced a changing magnetic field, which in turn had to induce a changing magnetic field, and so on. The field would radiate outward in all directions having the property of waves. Maxwell had predicted the existence of electromagnetic radiation.
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- When Maxwell took the ratio of the constants for electric charge and magnetic force he got a familiar number:
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---------------------------------- 1 / kC * kB = 9 meters^2 / seconds^2
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- This happens to be the speed of light squared.
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- The ratio of the electric and magnetic constants is equal to the speed of light squared.
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------------------------------------ C^2 = 1 / kC * kB
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------------------------------------ where: kC = 8.85417817 * 10^-12 farads / meter
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------------------------------------ kB = 1.256637061 * 10^-6 henrys / meter
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------------------------------------ c^2 = 1 / 8.85417817 * 10^-12 farads / meter * 1.256637061 * 10^-6 henrys / meter
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------------------------------------ c^2 = 1/11.1265 * 10^-18 farad * henry / meter^2
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----------------------------------- farad = coulomb / volt
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----------------------------------- henry = weber / ampere
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---------------------------------- weber = volt / sec
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--------------------------------- coulomb = ampere * second
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- Farad is a charge of one coulomb with a potential difference of one volt.
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- Henry is the inductance of one closed loop that has one weber of magnetic flux for each ampere of current.
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- Weber is the electromotive force of one volt when the magnetic flux is reduced to zero in one second.
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- Coulomb is the charge of one ampere of current moving in one second.
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- It all cancels out and we are left with:
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--------------------------------- c^2 = 8.9876 * 10^16 meters^2 / sec^2
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-------------------------------- c = 299,792,458 meters / second , the speed of light in a vacuum
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- Maxwell arrived at this just through his equations that described the forces of electricity and magnetism. He saw the light through the math, so always do the math.
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- This is too much to be a coincidence. Maxwell concluded that light must itself be an electromagnetic radiation. An explanation for the exact manner in which light waves, with frequencies of hundreds of trillions, could be produced electromagnetically had to wait another 50 years.
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- Quantum theory was developed and applied to a new understanding of the internal structure of the atom. Maxwell used his intuition and visualization through his equations to come to the right conclusion 50 years before anyone knew how electromagnetic radiation was produced.
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- He thought that light must be generated by an oscillating electric charge. And, since the electric charges oscillation could be at any velocity, there must be a whole family of electromagnetic radiation at different frequencies, yet remaining to be discovered. ( See Review 36 “ The Electromagnetic Spectrum”)
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---------------
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- Footnote (1) - Hans Christian Oersted was a Danish physicist born in 1777. He went to the university of Copenhagen and got is Ph.D in philosophy in 1799. Hans younger brother became the prime minister of Denmark. Hans became famous by observing that current through a wire deflected a compass needle at right angles to the direction of current. Reverse the direction of current and the needle points in the opposite direction. Hans published his works in 1820 and set of an explosion of activity from Coulomb, Ampere, Faraday, and Henry.
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- Footnote (2) - Joseph Henry was an American physicist born in Albany, New York in 1797. He was an apprentice to a watchmaker and age 16. He broke into a church and started reading books that he found there. He entered Albany Academy and eventually taught math and science there.
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- In 1829 Henry heard of Oersted’s experiment and tried to build an electromagnet himself. He wanted to make it bigger but copper wires kept shorting out. Henry decided to use insulation made from his wife’s silk petticoat. In 1831 he demonstrated he could lift 750 pounds with his homemade magnet.
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- In 1832 he did a demonstration at Yale University lifting more than a ton of iron using an ordinary battery. Henry went on to invent the electrical relay and eventually the telegraph. He published a paper describing how to make an electric motor. Michael Faraday had a similar paper describing the electric generator.
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- In 1848 Henry projected the Sun’s image on a screen and made sensitive measurements to show that sunspots were cooler than the rest of the Sun. He became the first secretary of the Smithsonian Institute. He was one of the founders of the National Academy of Sciences.
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- Using his telegraph he started a weather system that eventually became the United States Weather Bureau. The President of the United States, Rutherford, B. Hayes, attended his funeral in 1878 to honor this great US citizen.
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To learn something new each day is half the cure of ignorance. To teach someone something each day is the other half of the cure.
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- March 15, 2019
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