- 3209 - SOLAR WIND - enters Earth’s magnetic field? How does the Earth’s magnetic field protect us from the Solar Wind? This review has the physics and math to explain how the Solar Wind of charged particles are captured by the Earth’s magnetic field. The charges bounce between the North and South magnetic poles and create the Van Allen Radiation Belts that are far above our heads and shielding us from the Sun’s more dangerous radiation.
------------------ 3209 - SOLAR WIND - enters Earth’s magnetic field?
- The solar wind is a constant stream of charged particles coming from the Sun. The Earth is a giant bar magnet and when these particles reach the Earth they are trapped in our magnetic fields high above the atmosphere.
-
- If the Solar Wind was allowed to reach the surface life would suffer serious radiation damage and likely extinction. Both our magnetic field and our dense atmosphere are what protects us.
-
- To learn the physics on how this works let’s take one proton, that is a high energy ionized nucleus of a hydrogen atom, and have it coming from the Sun with a cloud of particles striking the Earth at an angle of 40 degrees. The proton is traveling 33,555,000 miles per hour. Will it be captured by the Earth’s magnetic field. The strength of the magnetic field is 10^-5 Tesla, (0.00001 Tesla).
-
- To figure this out we need to study electric charges and magnetism in the laboratory. One of the laboratories tools is a common Cathode Ray Tube, like the CRT’s in old televisions. The electronic beam is bent by the magnetic forces inside the tube.
-
- The speed of the electron and the force at right angles that is causing its path to the screen to bend is precisely measured. The magnetic force is acting at right angles to the path of the speeding electron. Of course, the charge of an electron is exactly the same as the electric charge of a proton which is in the Solar Wind .
-
- The amount of magnetic force on the moving electron is directly proportional to the amount of electric charge, the velocity of the moving electric charge, and the strength of the magnetic field.
-
------------------------- F = q * v * B
-
------------------------ To make these proportions an equality we must choose the proper units of measurement for the equation. The Force is in Newtons, or, kilogram* meters^2 / seconds^2.
-
------------------------ The electric charge of the electron, “q”, is 1.6 * 10^-19 Coulombs. The Coulomb is defined as the amount of a moving charge of one ampere of current moving for one second. One Coulomb is equivalent to the charge from 16,000,000,000,000,000,000 electrons. That is 1.6 * 10^19 electrons.
-
------------------------- The units for the strength of the magnetic field, “B”, is Tesla. One Tesla is equal to one kilogram / Coulomb-second. ( Another common unit for “B” is Gauss, which is equal to 0.0001 Tesla. That is 10,000 Gauss = one Tesla.)
-
------------------------ The velocity, “v”, is in meters per second.
-
- To get an understanding of the strengths of magnetic fields:
-
---------------------- Interstellar space , --------------------- B = 10^-10 Tesla.
--------------------- Near the surface of Earth, ------------ B = 5 * 10^-5 Tesla. (0.00005 Tesla)
-
--------------------- A refrigerator magnet, ------------------ B = 0.01 Tesla
-
--------------------- Near the magnet poles, ------------------- B = 0.01 Tesla
-
--------------------- Near the surface of a Neutron Star, ------ B = 100,000,000 Tesla
-
-------------------- Near the surface of an atomic nucleus, -- B = 10^12 Tesla.
-
- An electrostatic charge also has the force of an Electric Field which is directly proportional to the electric charge, “q”, and the Electric Field strength, “E”.
-
------------------------- F = q * E
-
- Because the force of the electric field generated by the moving electric charge is at right angles, or perpendicular, to the magnetic field the moving charge tends to go in a circle, or spiral in its path forward.
-
- When this happens we have another force called Centripetal Force that is directed to the center of the circle. The force is equal to mass * acceleration. And, the acceleration of circular motion is equal to the tangential velocity^2 / radius.
-
--------------------------- F = m * a
-
--------------------------- a = v^2 / R
-
--------------------------- F = m * v^2 / R
-
- Because the Force due the magnetic field and the force due to the Centripetal Force must be in balance if the spiraling electric charge is stable in its path forward, then:
-
-------------------------- F = q * v * B = m* v^2 / R
-
- Solving for the radius, R in the above equation:
-
-------------------------- R = m * v / q * B
-
--------------------------- “m * v“, is (mass * velocity) which is the momentum of the moving charge. “q * B” is the strengths of the two right angle forces of the electric charge and the magnetic field.
-
- Now, let’s get back to that proton in the Solar Wind striking the Earth at an angle of 40 degrees and traveling at 33,555,000 miles per hour. Will the proton be captured by the magnetic field lines that are in the Van Allen Belt about 1,800 miles above the Earth. At that elevation the strength of the Earth’s magnetic field is , B = 10^-5 Tesla.
-
------------------------------ B = 10^-5 Tesla
-
------------------------------ q = 1.67 *10^-19 Coulombs
-
------------------------------ v * (sin 40) = 1.5 * 10^7 meters / second * (0.64) = 10^7 meters / second, the velocity that is perpendicular to the Earth’s magnetic lines of force.
-
------------------------------ m = 1.67*10^-27 kilograms, the mass of a proton.
-
- Substituting these values into -------------------------- R = m * v / q * B:
-
- We get a radius of 10 kilometers for the spiraling proton as it travels along the magnetic lines of force towards the Earth’s South Magnetic Pole. The altitude of the Van Allen Belt magnetic field is 1,800 miles, or 3,000 kilometers. So, the proton is easily captured with its 10 kilometer spiral.
-
- If the proton was not heading toward the Earth it would still be traveling in the magnetic fields of interstellar space. We mentioned that the strength of the magnetic field in the Milky Way Galaxy is , B = 10^-10 Tesla. A proton traveling through the galaxy would drift in a giant circle due to this galactic magnetic field. The radius of the Milky Way Galaxy is 5 * 10^21 meters
-
- What momentum would the proton have to have to escape the Galaxy?
-
- Substituting these values into -------------------------- R = m * v / q * B :
-
----------------------- m *v = (5*10^21meters) * ( 1.6*10^-19 Coulombs) * ( 10^-10 Tesla)
-
----------------------- m *v = 8 *10^-8 kilogram * meters / second.
-
- For a particle the size of the proton this is an exceedingly high momentum. Since we used the radius of the galaxy in our calculation a momentum greater than this would have the escape velocity needed to leave the galaxy. Therefore, we would expect that Cosmic Ray protons striking the earth to have a lower momentum than this, assuming they came from inside the Milky Way Galaxy.
-
- To compare this proton momentum, m *v = 8 *10^-8 kilogram * meters / second, to the fastest proton momentums we can produce in the Fermi Lab particle accelerator, it is 100,000,000 larger. Fermi Lab momentum = 5 * 10^-16 kilogram * meters / second.
-
- The proton traveling from the Sun has far less momentum:
-
- Substituting these values into -------------------------- R = m * v / q * B:
-
----------------------- m *v = (1,000 meters) * ( 1.6*10^-19 Coulombs) * ( 10^-10 Tesla)
-
----------------------- m *v = 1.6 *10^-26 kilogram * meters / second.
-
- The Solar Wind proton is easily captured by the Earth’s magnetic field. Its path follows the magnetic lines towards the poles. As the path approaches the poles all the magnetic lines of force come together like a giant bar magnet.
-
- The magnetic lines of force are “pinched” together. When the spiraling proton encounters this pinch it bounces off reversing direction and begins spiraling toward the opposite pole where the same thing happens. The captured proton bounces back and forth between the Earth’s magnetic poles.
-
- The captured protons form a shield above the Earth called the Lower Van Allen Radiation Belt that is about 1,800 miles above the Earth. This is a region of very high radiation and astronauts crossing it must have protective shielding.
-
- The same process occurs with negatively charged electrons that are part of the Solar Wind. Electrons are 1,860 times lighter than protons and these captured negatively charged particles create a Higher Van Allen Radiation Belt. This region is about 9,300 miles above the Earth.
-
- When these high energy particles reach the lower elevations at the North and South Poles they strike gas atoms in the atmosphere and create the Northern and Southern Lights, the Auroras.
-
- The next time you see this beautiful, colorful light show you can think of those spinning protons spiraling into the magnetic pole and bouncing backwards to reverse directions along the magnetic lines heading for the South Pole.
-
- Since we know the radius of the spirals we can even calculate how fast the protons are spinning. It is about 9,000 rpm, revolutions per minute. Here is the calculation:
-
----------------------- Circumference of the spiral = 2 * pi * Radius
-
----------------------- Period of the spiral = 2 * pi * Radius / velocity
-
---------------------- Radius = R = m * v / q * B
-
----------------------- Period = 2 * pi * m / q * B
-
----------------------- Frequency = 1 / Period = q * B / 2 * pi * m
-
----------------------- f = ( 1.6*10^-19 Coulombs) * ( 10^-5 Tesla) / 2 * pi * ( 1.67 * 10^-27 kilograms)
-
-------------------------f = 150 cycles per second
-
- The proton is spiraling around the magnetic lines of force at 150 times per second.
-
------------------------- Other Reviews to learn more:
-
- 1245 to learn about the dust in space. Can Dust in Outer Space contain Life? What creates the dust we find in space throughout our Solar System? Could life have started in the dust of outer space? Once life got started in space how did it survive the radiation that destroys life? Regardless of how we got here aren’t you glad you landed on Mother Earth?
-
- 1246 - Radiation in Space and Dangers to Life. Space may have the ingredients for the start of life but, it also has the radiation to destroy life. See Review 1245 - Dust in Space Ingredients for Life. We do not know when chemistry became biology, but, when life leaves the protection of Earth it enters a space bathed in radiation that can destroy life.
-
- 1247 to learn about the Solar Wind. The Solar Wind Dangerous, or, a new Form of Energy? The Solar Wind gets captured by the Earth’s magnetic field creating a powerful source of electricity high above out heads. Is there a way to tap into all this energy that the Sun sends us.
-
- July 4, 2021 SOLAR WIND - enters Earth’s magnetic field? 1248 3209
----------------------------------------------------------------------------------------
----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
--------------------- --- Monday, July 5, 2021 ---------------------------
No comments:
Post a Comment