Orthogonal Magnetic Field

[Cherie Trojak]

Myteacher discussed this illustration in class where there were 2 perpendicular magnetic fields. He said that they both cancel each other out. I didn't understand it. I tried to understand it by literally finding out the direction of the magnetic field lines. I'll just attach the illustration here for more clarity.

He said that the magnetic field of those two straight wires cancel each other out. I don't understand what that means. Using the right hand thumb rule, the magnetic field due to one of the wires is perpendicular to the magnetic field due to another straight wire.

If there is a second (perpendicular) wire with same the current but in opposite direction, the magnetic field will vanish at the half distance between the two wires, because each wire will generate a magnetic field of same strength, but in opposite directions (which you can also see with the right hand thumb rule).

Either your teacher is wrong or you misunderstood them. Perhaps they meant that those two straight sections have no bearing on the magnetic field at the center point of the two curved regions (point C). That's the most reasonable guess I can make.

Also, recall that we have already proven that neither the electric nor magnetic field have any components in the direction of wave propagation (z-direction in this case). Therefore, there is no z-component for magnetic field. However, there potentially exists (as of the moment) a component of B in the direction of E (the x-direction). We aim to prove that such an occurrence is not possible.

We now recognize that for the above statement to be true, the i component on the right hand side of the equation must be zero for all values of z and t. The only way for this to be possible is if the magnetic field (B) has no component in the direction of the x-axis (B sub x = 0). Therefore, the magnetic field (B) can have no component in the direction of the electric field (E) and hence E and B are mutually orthogonal.

The terms on the left and right side of the equation (kE and omega B) are effectively the amplitudes of the electric and magnetic fields respectively. Being that they are equal we realize that the amplitudes of the electric and magnetic fields are also equal for an electromagnetic wave.

Taking note of the fact that omega divided by k is the velocity of a sinusoidal wave, as well as the fact that electromagnetic waves propagate at the speed of light, we arrive at the following relationship:

In physics, a radio wave, indeed all EM radiation is called a transverse wave, meaning, by definition, that the oscillations of the waves are perpendicular to the direction of energy transfer and travel.

The electric and magnetic parts of the field stand in a fixed ratio of strengths in order to satisfy the two Maxwell equations that specify how one is produced from the other. These $\mathbfE$ and $\mathbfB$ (in physics the magnetic part uses B for some reason, I'll maintain that convention to make it easier for the physics folks to correct any errors) fields are also in phase, with both reaching maxima and minima at the same points in space.

Ask James Clerk Maxwell; his electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:

These solutions represent planar waves traveling in the direction of the normal vector n. If we define the z direction as the direction of n. and the x direction as the direction of E., then by Faraday's Law the magnetic field lies in the y direction and is related to the electric field by the relation $\scriptstyle c^2\partial B \over \partial z \,=\, \partial E \over \partial t$. Because the divergence of the electric and magnetic fields are zero, there are no fields in the direction of propagation.

For radiated fields, the electric field (E) and (H) are always perpendicular. No one knows why this is more than we know any other physical law, but so far as anyone can demonstrate, it's always true. As WPrecht says, Maxwell's equations require electromagnetic waves to be this way. There's also simpler, albeit less complete mathematical explanation: the Poynting vector. This vector is simply the cross-product of E and H:

This vector S represents the direction of energy transfer, so it follows that if the energy is radiating away, then the electric and magnetic fields must be mutually perpendicular to this, by the definition of the cross product operation.

You can gain some intuition into why this is true by considering the fields around a dipole. Say the dipole is vertical. The electric field lines are vertical, because the voltages are different along the length of the dipole. Meanwhile, current is flowing through the dipole, and current through a conductor makes magnetic field lines in concentric circles around that conductor. The result looks like this:

(Here they've used B for the magnetic field instead of H. There's a difference, but it will send us off on a tangent. Without compromising the understanding of this particular problem you can consider them to be the same.)

If you think more about it, all moving electric charges, not just those in wires, create an associated magnetic field. This includes the displacement currents involved in radiation. And really, create might be the wrong word, because time-variant magnetic fields are also associated with electric fields (see Faraday's law). That magnetic fields can create electric fields and electric fields can create magnetic fields is what allow these two to self-propagate indefinitely in free space. Of course you can have electric fields with no magnetic field (capacitors) or magnetic fields with no electric fields (inductors), but these don't radiate (in the ideal case). So, the perpendicular arrangement of the fields in a dipole isn't coincidence: it's what makes it an effective antenna.

The two fields do not have to be orthogonal, and in the diagram posted they are in fact NOT orthogonal everywhere (for example, what do E and H do near the ends of the antenna?). Orthogonal E and H field are the property of a propagating EM wave in free space. Around an antenna, within a few wavelengths distance, there are "near field" or "Fresnel" regions in which there are non-propagating waves. These waves do not have necessarily orthogonal fields. More detail can be found in a reference text such as Antenna Theory by Balannis.

Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.

There are two different, but closely related vector fields which are both sometimes called the "magnetic field" written B and H.[note 1] While both the best names for these fields and exact interpretation of what these fields represent has been the subject of long running debate, there is wide agreement about how the underlying physics work.[7] Historically, the term "magnetic field" was reserved for H while using other terms for B, but many recent textbooks use the term "magnetic field" to describe B as well as or in place of H.[note 2]There are many alternative names for both (see sidebars).

Here F is the force on the particle, q is the particle's electric charge, v, is the particle's velocity, and denotes the cross product. The direction of force on the charge can be determined by a mnemonic known as the right-hand rule (see the figure).[note 3] Using the right hand, pointing the thumb in the direction of the current, and the fingers in the direction of the magnetic field, the resulting force on the charge points outwards from the palm. The force on a negatively charged particle is in the opposite direction. If both the speed and the charge are reversed then the direction of the force remains the same. For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left. (Both of these cases produce the same current.) On the other hand, a magnetic field combined with an electric field can distinguish between these, see Hall effect below.

The field can be visualized by a set of magnetic field lines, that follow the direction of the field at each point. The lines can be constructed by measuring the strength and direction of the magnetic field at a large number of points (or at every point in space). Then, mark each location with an arrow (called a vector) pointing in the direction of the local magnetic field with its magnitude proportional to the strength of the magnetic field. Connecting these arrows then forms a set of magnetic field lines. The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and the local density of field lines can be made proportional to its strength. Magnetic field lines are like streamlines in fluid flow, in that they represent a continuous distribution, and a different resolution would show more or fewer lines.

Various phenomena "display" magnetic field lines as though the field lines were physical phenomena. For example, iron filings placed in a magnetic field form lines that correspond to "field lines".[note 5] Magnetic field "lines" are also visually displayed in polar auroras, in which plasma particle dipole interactions create visible streaks of light that line up with the local direction of Earth's magnetic field.

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