# on video The Electromagnetic field, how Electric and Magnetic forces arise

The interactions of electricity and magnetism are difficult to explain in nontechnical terms. This is primarily because one has to describe the interactions in terms of invisible "force fields" which shift, expand, contract, strengthen, weaken, and rotate in space, and these are very difficult to adequately describe in verbal terms. In mathematical terms, coupled sets of three-dimensional vector differential equations are required, and these are also quite difficult to visualize.

So, we will go light on the mathematics as we discuss E & M. We will rely on more intuitive, graphical interpretations. Here are the basics:

Electric field for two equal but opposite charges. The electric force at any point P is tangent to the electric field.

Magnetic field around a bar magnet. Note the close similarity to the electric field in the previous illustration.

1) The electric force is created by electric charges. For all practical purposes, the world around you contains only two types of charged particles: protons, which have a charge of +1 in atomic units, and electrons, which have a charge of -1. There are many hundreds of other charged particles, but nearly all of them are unstable and disintegrate on time scales shorter than a billionth of a second. Like energy and momentum, the total charge of the Universe is conserved. You can create or destroy positive charge as long as you also create or destroy an equal amount of negative charge, but the algebraic total cannot change. As far as we know, the total electric charge in the Universe is exactly zero.

The electrostatic force between two point charges is given by Coulomb's Law:

F = k q1 q2 / r2

where: k = the electrostatic constant = 8.99 X 109 kg m3 / s2 coul2, r = the distance between the two charges, and q1 and q2 are the two charges, measured in coulombs. (One coulomb = the charge on 6.24 X 1018 electrons. Therefore, one proton or electron carries a charge of ±1.602 X 10-19 coulomb.) If q1 and q2 have the same sign, the electrostatic force is repulsive. If they have opposite signs, the force is attractive. Notice how the formula for electrostatic force looks exactly like that for gravity: all we have to do is substitute the gravitational constant G for the electrostatic constant k, and switch mass for charge.

2) Static magnetic fields are not described by a simple formula, because magnets always have a north pole and a south pole, so the magnetic field always loops from one pole to the other. If one immerses a magnet in a heavy fluid which contains iron filings, and shakes the container, the iron filings will align themselves along the magnetic field and thus reveal the shape of the field. The field shown at right is the simplest possible magnetic field. Both this and the field shown in the previous illustration are called dipole fields, because they are created by two poles.

Although there is no simple formula for magnetostatic force, there is a magnetic force constant "m" which is analogous to "k" for electric fields and to "G" for gravity. m is equal to 1.26 X 10-6 in metric units.

3) Electricity and magnetism are essentially two aspects of the same thing, because a changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. (This is why physicists usually refer to "electromagnetism" or "electromagnetic" forces together, rather than separately.)

To demonstrate that an electric current (i.e., moving electric charge) generates a magnetic field, all you need to do is simply place a magnetic compass next to a wire in a circuit. When current is passed through the wire, the compass will deflect, indicating the presence of a magnetic field circling the wire. (In fact, this is exactly how the magnetic field of a current was discovered. In 1819, Professor Hans Oersted of the University of Copenhagen was giving a lecture on electric currents and also on magnets. He happened to leave a next compass to a conducting wire, and in the middle of the lecture he noticed that the current was deflecting the compass. This is probably the only important physics discovery ever made before a live audience.) It is important to understand that the Coulomb force law only provides the full story of the forces between two charges when the charges are standing still. (That's why it's referred to as an electrostatic force law.) The forces between moving electric charges are much more complicated, and in fact, what we call a "magnetic field" is actually just the result of moving charges acting on each other. Static magnetic fields in materials such as iron are more-or-less caused by the motion of electrons within atoms.

One can also use a magnet and some loops of wire to demonstrate the reverse of the above: that a changing magnetic field creates a current. (This is called induction.) By simply moving a magnet through a coil of wire, one can easily detect the current flowing in the coil by using a sensitive ammet

The interactions of electricity and magnetism are difficult to explain in nontechnical terms. This is primarily because one has to describe the interactions in terms of invisible "force fields" which shift, expand, contract, strengthen, weaken, and rotate in space, and these are very difficult to adequately describe in verbal terms. In mathematical terms, coupled sets of three-dimensional vector differential equations are required, and these are also quite difficult to visualize.

So, we will go light on the mathematics as we discuss E & M. We will rely on more intuitive, graphical interpretations. Here are the basics:

Electric field for two equal but opposite charges. The electric force at any point P is tangent to the electric field.

Magnetic field around a bar magnet. Note the close similarity to the electric field in the previous illustration.

1) The electric force is created by electric charges. For all practical purposes, the world around you contains only two types of charged particles: protons, which have a charge of +1 in atomic units, and electrons, which have a charge of -1. There are many hundreds of other charged particles, but nearly all of them are unstable and disintegrate on time scales shorter than a billionth of a second. Like energy and momentum, the total charge of the Universe is conserved. You can create or destroy positive charge as long as you also create or destroy an equal amount of negative charge, but the algebraic total cannot change. As far as we know, the total electric charge in the Universe is exactly zero.

The electrostatic force between two point charges is given by Coulomb's Law:

F = k q1 q2 / r2

where: k = the electrostatic constant = 8.99 X 109 kg m3 / s2 coul2, r = the distance between the two charges, and q1 and q2 are the two charges, measured in coulombs. (One coulomb = the charge on 6.24 X 1018 electrons. Therefore, one proton or electron carries a charge of ±1.602 X 10-19 coulomb.) If q1 and q2 have the same sign, the electrostatic force is repulsive. If they have opposite signs, the force is attractive. Notice how the formula for electrostatic force looks exactly like that for gravity: all we have to do is substitute the gravitational constant G for the electrostatic constant k, and switch mass for charge.

2) Static magnetic fields are not described by a simple formula, because magnets always have a north pole and a south pole, so the magnetic field always loops from one pole to the other. If one immerses a magnet in a heavy fluid which contains iron filings, and shakes the container, the iron filings will align themselves along the magnetic field and thus reveal the shape of the field. The field shown at right is the simplest possible magnetic field. Both this and the field shown in the previous illustration are called dipole fields, because they are created by two poles.

Although there is no simple formula for magnetostatic force, there is a magnetic force constant "m" which is analogous to "k" for electric fields and to "G" for gravity. m is equal to 1.26 X 10-6 in metric units.

3) Electricity and magnetism are essentially two aspects of the same thing, because a changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. (This is why physicists usually refer to "electromagnetism" or "electromagnetic" forces together, rather than separately.)

To demonstrate that an electric current (i.e., moving electric charge) generates a magnetic field, all you need to do is simply place a magnetic compass next to a wire in a circuit. When current is passed through the wire, the compass will deflect, indicating the presence of a magnetic field circling the wire. (In fact, this is exactly how the magnetic field of a current was discovered. In 1819, Professor Hans Oersted of the University of Copenhagen was giving a lecture on electric currents and also on magnets. He happened to leave a next compass to a conducting wire, and in the middle of the lecture he noticed that the current was deflecting the compass. This is probably the only important physics discovery ever made before a live audience.) It is important to understand that the Coulomb force law only provides the full story of the forces between two charges when the charges are standing still. (That's why it's referred to as an electrostatic force law.) The forces between moving electric charges are much more complicated, and in fact, what we call a "magnetic field" is actually just the result of moving charges acting on each other. Static magnetic fields in materials such as iron are more-or-less caused by the motion of electrons within atoms.

One can also use a magnet and some loops of wire to demonstrate the reverse of the above: that a changing magnetic field creates a current. (This is called induction.) By simply moving a magnet through a coil of wire, one can easily detect the current flowing in the coil by using a sensitive ammet

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