# The Magnetic Field

In Section 4.1 we defined the electric field that manifests the electric force. The electric field exists as a vector at every location in space. Similarly, we can define a magnetic field to explain how magnets interact with each other. Like in electricity, the magnetic field is defined as a vector at every point in space, and (for historical reasons) is represented by the symbol $$\vec B$$. As a vector, of course, it has both strength and direction:

## Strength

The SI unit of the magnetic field is the tesla (T). One tesla is a fairly large field, such as you'd find close to a strong rare-earth magnet (such as you'd find in a loudspeaker) or in a modest MRI machine. A refrigerator magnet creates a field of milliteslas close to its surface. The Earth itself has a magnetic field that is around 50µT at its surface, which we might consider the "background field" we all live in.

The largest continuous magnetic field created by humans as of 2015 is only 45T. Stronger fields can be created for short periods of time: the MagLab at Los Alamos can create a pulsed magnetic field of 100.75T. The largest field ever created by humans was 2800T by VNIIEF in Sarov, Russia; it involved explosives and partially destroyed the apparatus. In space, much stronger magnetic fields can be found. Neutron stars can have a surface magnetic field between 1 million and 100 billion tesla.

## Direction

The electric field at a location points in the direction a positive charge would feel a force in, if it were at that location. Because there are no magnetic charges (monopoles), the magnetic field's direction is defined in terms of the magnetic dipole instead:
The magnetic field vector points in the direction a magnetic dipole would point.

(Instead of asking WWPD, we can ask WWCD: "What would a compass do?")

In the diagram below, see if you can figure out the direction of the magnetic field at each of the circled numbers, and then click on the number to see if you're right. Remember that like poles repel and unlike poles attract.
You can connect these arrows smoothly to draw magnetic field lines, just as we drew electric field lines, as in this figure. Notice that the field looks a lot like the field of an electric dipole, with its "lobes" above and below.
What is the magnetic field inside the bar magnet, at its center?
to the left ← zero to the right →
For an electric dipole, the electric field at the star would point to the right. But a magnetic dipole is different, and we can explain this result in two ways:
• Electric field lines start at positive charges and end at negative charges, but there are no magnetic charges, no monopoles. Thus magnetic field lines never begin or end; they form loops, or come in from infinity and go out to infinity. So the field lines which enter into the magnet through the S pole cannot stop, but keep going until they pass out of the N pole. Thus the magnetic field at the star must point to the left.
• We mentioned earlier that we can think of magnetic poles as sides of a coin, and so a bar magnet is like a stack of coins. At the center of that stack, if you look to the left, you see an S pole, and to the right is an N pole. Thus a compass needle placed at the star would point to the left (towards the S pole).

It's worth repeating from the example:
Magnetic field lines never begin or end.