Magnetic Fields

A bar magnet is approaching to a welding arc. As a result of this the welding arc is distracted. Watch yourself in the short film.

Magnetic forces always occur pairwise. So beside the bar magnet there must be a second magnetic field. That is the point. Where is it?

By the way: There is an attraction between the N-pole and the S-pole. But same poles do repell each other. The earth acts as if there is a huge bar magnet inside it. The N-pole of a bar magnet will be attracted toward the northern hemisphere. So there must be a imaginary S-pole far north.

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Even some people state to be sensitive to a magnetic field, humans do not have any sensors for the magnetic field. But we are able to recognize the forces of a magnetic field: a compass or a magnet holding something on the steel dor of the fridge.

The magnetic field pattern can made be visible with iron fillings on top of a horse-shoe magnet. In between is a homogeneous field, outside we are talking of inhomogenous field. The field lines do have a direction since the iron fillings will move as you start to move the magnet.

The stronger the magnetic field, the more densely packed the lines of flux. So we describe the strength of the magnetic field by the magnetic flux density B, which is measured in Tesla (T).

Around a long straight wire with a current flow inside we observe a circular magnetic field. However to observe this there is current of at least 20 A necessary.

If you use magnet neadels instead of iron fillings, you will notice a change in direction if the direcetion of current changes. This leads to the right-hand grip rule:

If your right thumb points in the direction of the current, your fingers then curl in the direction of the lines of flux.

Around a wire the magnetic flux density decreases with the distance $r$: $B=\frac{\mu_0 I}{2\pi r}$, in which the constant $\mu_0=4\pi \cdot 10^{-7}~TmA^{-1}$ is the permeability of free space.

If you wrap a long wire we are talking of a coil. A solenoid is a long coil with a large number of turns of wire. The result of the superposition of each magnetic field is a homogeneous field pattern inside the solenoid. The pattern is identical to the field of a bar magnet. The difference: We can switch it on/off and adjust the strength of the magnetic field.

The stronger the current $I$ and the more turns of wire $n$ the stronger the magnetic flux density. If a solenoid is in a vacuum or air we can write:

Electrons spin in each atom. So each electron acts like a tiny electric current and produces a tiny magnetic field. In some materials the magnetic effects of all electrons cancel in other they line up. In ferromagnetic materials like iron, cobalt and nickel the tine magnetic fields line up to a strong magnetic field.

So a ferromagnetic core in a solenoid increases the magnetic strength. With the permeability of materials $µ_r$ which is up to 10,000 for iron, 1 in vacuum and less then 1 for copper we can write:

A wire carrying current placed in a magnetic field feels a force. The two magnetic fields interact with each other. If the direction of the two patterns are opposite the fields are destructive. If the direction is identical they line up constructive to a strong field resulting in a force on the wire. We can construct the direction of force with the right hand rule and the knowledge that densly packed field lines result in a pushing force.

The stronger the magnetic flux density $B$, the higher the current $I$, the larger the length $l$ of the conductor in the field and the more vertical the angle $\theta$ between the magnetic field and the conductor the greater the force $F$: $$F=B\cdot I\cdot l\cdot sin~\theta$$

Charged particles from the outer space get trapped by the magnetic field of earth and produce the spectacular glow in the sky shown in the video. The force (Lorentz) on a moving charge with its charge $Q$, velocity $v$ and angle $\theta$ can be written to: $$F=B\cdot Q \cdot v \cdot sin~\theta$$

ideas of
R. Brugger, FTA15 Elektronikschule Tettnang
K. Johnson et al., "Advanced Physics for You"