Magnetic Field Our planet's magnetic field is in a constant state of change, say researchers who are beginning to understand how it behaves and why. Above: potential energy plots for arrangements of 4 charges - 2 positive charges (red centres) and 2 negative charges (blue centres) of equal magnitude.
On the bottom-left are two positive charges in RGB, illustrating a common equipotential, in green, enclosing both charges.On the bottom-right a positive charge (red centre) is shown opposite a negative charge (blue centre) of equal magnitude. The charged particles in this plot will tend to move so as to occupy regions of low potential - the  two particles of like charge (above left) are essentially sitting on a 'hill' and will tend to 'roll-away' or move apart from one-another. The plots shown on this page do not plot the force, nor the field strength, since these are vector fields and we would have to indicate direction as well as magnitude, so, for simplicity, we have plotted the electric potential, phi, given by equation 5.
Electric Force on Moving ChargesIf we have a beam of moving charges, such as a beam of electrons (each of which has a mass M and negative charge of magnitude q) moving between two charged metal plates, then the beam will be deflected toward the plate of opposite charge (opposite charges attract!).
The Magnetic ForceMagnetism has some similarities to the electric force and the two are intimately connected.
Motion of Charged Particles in Magnetic FieldsTo calculate the trajectory of a charged particle moving in a magnetic field, we need a coordinate system for our vectors! An example of a magnetic field is illustrated below: electric charge (taken as positive by convention, though in reality it is the negative electrons which move in the opposite direction) flowing in an electrical wire as shown by the blue arrow generates a magnetic field which loops around the wire in the direction shown (red circular arrows). The radius of gyration, the radius of the helix, is given by r; P is the period (time taken) for the electron to complete one revolution of the helix and dx is the distance moved along the x-axis during one complete turn.
When the field-lines converge towards the poles, this indicates a strengthening of the magnetic field in this region.
Energized particles and electromagnetic waves are filtered through it towards the Earth, colliding with the ionized atoms of hydrogen, oxygen, and helium in the atmosphere, generating interactions and  chemical reactions in the atmosphere.
This interaction will have a plasma convection behavior as well, as energized parts will be pushed towards Earth, while less energized particles seek out the field of the Earth, being trapped by the magnetic field. This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. On this scale green represents zero potential, such as the points at which the negative and positive charge potentials cancel. On this RGB scale green illustrates values close to zero, where the positive and negative potentials cancel one-another.Remember electric charge comes in two 'flavours' - negative (-) and positive and like charges (- and - or + and +) repel whereas opposite charges (- and + or + and -) attract! The particles of opposite charges, above right, will tend to be attracted to the region of low potential between them - unlike charges attract!Electric charges are surrounded by electric fields which exert forces on other nearby electric charges.
Like the electric force, magnetism appears to have two 'flavours' - opposite poles of two bar magnets (north and south magnetic poles) will attract each other,  whilst like poles repel. The trajectory is plotted below using parametric equations (parameter t) with the radius of the helix in the y(t) direction. According to classical physics, an accelerating charged particle (remember that in physics acceleration can be a change in speed or a change in direction) emits electromagnetic radiation ('light') as photons (particles of light). The Earth acts like a giant bar magnet - it has a magnetic north pole (near to its geometric South Pole) and a magnetic south pole (near to its geometric North Pole). This causes the gyrating particles to gyrate in smaller orbits (radius of orbit, r is inversely proportional to B) and in such a non-uniform magnetic field the speed of the particles along the field-lines does change - it slows down (the right-hand rule indicates a force acting against the path of the helix).
It has been established that the outer space has an average temperature of 2.7 ° K (helium particles at these temperatures are superconductors) while the corona of stars can reach 1 million ° K. The RGB scale shows the highest charge region in red, the lowest in blue and the algorithm used highlights the contours (equipotentials).On the top-right, two positive charges are shown in an orange-blue scale. The electric force, F, is the product of the electric charge, q, and the electric field strength, E (equation 1 below). Moving electric charge generates a magnetic field and a magnetic field will accelerate moving electric charges.


Distance dx depends on the x-component of velocity (this is the velocity component parallel to B and this does not change) and if this is zero, then the particle traces a stationary circle.
Magnetic field lines connect these two poles in large hoops which collectively form a doughnut-shaped (toroidal or torus-shaped) magnetic field around the Earth, which diminishes in strength as we travel away from the Earth's surface into space. However, magnetic fields cannot alter the total speed of particles, as they cannot change the particles' kinetic energy, thus as the particles move slower and slower in the direction of the field line, they move faster and faster in their circular orbits. The electric field strength is then force per unit of charge (equation 2) meaning the force experienced on a unit test-charge placed in the electric field due to a second, central charge. One key difference is that the magnetic force is the vector cross-product between velocity of the charged particle and the magnetic field strength, B, multiplied by the electric charge (equation 6) - compare this with equation 1 for the electric force. This emission of radiation causes the gyrating particle to lose energy - it slows down and so the radius of the orbit decreases (the frequency remains unchanged) and in reality the radius of the spiral diminishes as the particle moves - the helix spirals down.
Eventually, the particles execute tiny stationary orbits at high speed and stop moving along the field-line and then their path reverses. If we are dealing with stationary charges (electrostatics) then the electric force between two such point charges is also called the Coulomb force. This vector cross-product means that the force acts in a direction which is at right-angles (perpendicular) to the direction of movement of the particle (given by the velocity vector) and the magnetic field.
The blue line represents the Earth's axis of spin, on which lie its geometric poles, and the magnetic field is tilted about 12 degrees relative to this spin-axis (though the field drifts and its angle of tilt changes noticeably every year).Magnetic field lines point from magnetic north to magnetic south - they have to be assigned direction, since the trajectory followed by electrically charged particles (the helices as illustrated above) depends on this direction. In the Van Allen belts, the particles oscillate back-and-forth between the poles once every 0.1-3 seconds!In addition to bouncing back-and-forth between the polar regions, the particles also drift in longitude (the field strength diminishes with distance from the Earth and eventually the field-lines become too weak to confine the particles which can then move from one field-line to another. The strength of the force decreases by an inverse-square law, meaning that as distance from the source charge is doubled, the force drops to a quarter of its strength. If both electric and magnetic forces act upon a particle, then the total force is given by the Lorentz force law (equation 7).
The radiation emitted is also known as cyclotron radiation.Note also, that if the sign of the electric charge on the particle is changed, then the sense of the helix is changed. Electric field lines similarly have direction - radiating out from a positive charge and inwards to a negative charge (so a positive test charge will follow the field lines). High-energy protons drift westward around the Earth every 0.1 s and lower-energy electrons drift eastward, circling the Earth once every 1 to 10 hours.
Looking along the helix from the origin the direction of B (positive x-axis in this case) a negatively charged particle is seen to spiral clockwise whilst a positively charged particle spirals anti-clockwise. One key difference, however, is that although it is easy to have a single electric charge, positive or negative, it is very hard, if not impossible, to have a single isolated magnetic pole (a monopole) and with a few possible extreme exceptions, a magnetic north is always accompanied by a magnetic south (a dipole).The presence of the Earth's magnetic field is thought to be due to electric charges flowing in the Earth's outer core, which appears to be a metallic liquid. These velocities are quite fantastic!The AuroraeThe inner radiation belt interacts with the Earth's upper atmosphere - lower energy electrons drop-out and collide with air molecules, exciting and ionising the molecules. Epsilon-zero, the curly 'e' with the zero subscript, is the permittivity of free space ( = 8.854 x 10^-12 C^2N^-1m^-2) or the ease with which the electric field traverses a vacuum and its value depends on the choice of units. In this way, the sign of the electric charge on the particle can be determined by analysing its path in a particle detector (such as a bubble chamber).Cyclotron radiation is seen in the magnetospheres of some planets where charged particles get trapped as they spiral along the planet's magnetic field, and also in stars, like the Sun and some neutron stars in X-ray pulsars. Rotation of the Earth sets up currents of moving charges inside this outer core and these charges generate a magnetic field. As the molecules de-excite they emit the excess-energy they gained in the collision as photons of light - the frequency and colour of the photons depends upon the element excited (mostly nitrogen or oxygen) and the flickering curtains of light produced in the upper atmosphere are known as the aurora borealis, or northern lights in northern latitudes, and the aurora australis, or southern lights, in southern latitudes.
The r-hat is a unit vector - force has magnitude and direction and this unit-vector indicates the direction of the force, which depends on the sign of the charge. If the field is sufficiently strong, then the charges will be confined by it, as they gyrate along the magnetic field lines, and the field is reinforced and achieves a fairly stable pattern - this is the electromagnetic dynamo theory.There is an additional complication to the shape of the Earth's magnetic field further from the surface - it gets distorted by the Solar wind and in the lee-side it is drawn out into a comet-shaped tail as it ploughs against the wind. The total force due to a collection of charges is equal to the spatial summation of the contributions to the force of each individual charge (equation 4).


This kind of radiation is often beamed in the direction of particle motion and has non-thermal characteristics. The Solar wind influences the aurorae - if the Solar wind increases in strength then it may supply more electrons to the Van Allen belts and it may also disturb the magnetic field, causing electrons to be dumped from the inner belt into the atmosphere - both effects will increase the aurorae.The Nature of Magnetism - it's all relative!Magnetism and electric phenomena are intimately connected, and yet it seems easier intuitively to understand electric charges and their electrical interactions than to conceptualise magnetism. Synchrotron radiation is emitted by many quasar nuclei - the nuclei of active galaxies that are thought to contain supermassive black holes (at the very least they do contain very strange objects!). Some of these particles leak through the magnetopause and become trapped in the Earth's magnetic field - gyrating along the magnetic field lines. These particles will gyrate around the arc of a field-line, travelling away from one pole and toward the other.
Charged particles trapped in the intense magnetic fields associated with black holes become accelerated to speeds approaching that of light!
This is fine where the magnetic field-lines are more or less parallel to one-another, as above the equator (a so-called uniform magnetic field) but towards the poles, the field-lines converge and get squeezed together. Particles gyrating along the field-lines into these regions experience another phenomenon - they are reflected to travel back along the field-lines in the opposite direction from which they came. Thus they bounce around between northern and southern latitudes, traveling as far poleward as they can before they are reflected, gyrating as they go. Bring the two wires near to each other - how will the magnetic fields interact?If the wires are parallel (side-by-side) and their currents flow in the same direction, then the wires will become attracted to one-another. Reverse the direction of flow of current in one of the two wires, so that the two currents flow in opposite directions, and the wires will repel one-another - like currents attract, unlike currents repel.
Imagine the electrons flowing from left to right along the wire and now imagine an electron outside the wire and flowing in the same direction and with the same speed as the electrons in the wire. This is like two wires with like currents - the electron will be attracted toward the wire. As opposite charges attract, and the electron is negatively charged, it as if the wire had somehow gained a net positive charge! Wires are made of metal, and metal atoms are electrically neutral - metals consist of a sea of delocalised electrons bathing a lattice of positive ions, but overall the net charge is zero. The wire still has a zero net electric charge!If the external electron is 'seeing' more positive charge in the wire, then it as if the number of positive ions (atom cores) per unit length of wire had somehow increased!
This could happen if the wire shrank and became shorter without effecting the flowing electrons - this would increase the density of positive ions in the wire, without increasing the total number - more positive charges cannot appear since electric charge is conserved - the net charge on the wire must remain zero and does so!
That's because length is relative!From the point of view of the electrons moving along, it is the wire that appears to be moving past them in the opposite direction. According to the Theory of Special Relativity moving objects become shorter in the direction of their motion. However, motion is relative - to the electrons the wire is moving and so the wire shrinks, but to the wire the electrons are moving and so they shrink and become closer together. Thus the electron 'sees' the wire shrink and increase its positive charge density and so the electron is attracted toward the wire by the electric force of attraction.
The wire 'sees' the distance between the electrons shorten, increasing electron charge density and the positive wire is attracted to this apparent increase in negative charge by the electric force.
The end result is that the wire and electron are attracted to one-another (but since the wire is much heavier it moves less and an experimenter in the lab will see the electron move toward the wire).The conclusion is surprising - electricity and magnetism are manifestations of the same fundamental force, the electromagnetic force, as seen from different points of view!



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