Magnetic Forces and Fields

Magnetic force and magnetic field definitions

We have to distinguish between a magnetic field and a magnetic force. We'll first define the magnetic force and then relate this to the magnetic field. The definition of the magnetic field is as below.

It is a force that only differs from other forces because it is generated by magnets. It is measured in Newtons$\left(\mathrm{N}\right)$like any other force. It is also important to note that the charged particle must be moving relative to the magnetic field for it to experience a magnetic force.

Relationship between magnetic force and magnetic field

We must now uncover how magnets create this force, and for this, we need to discuss the magnetic field. The definition of the magnetic field is as follows.

A magnetic field is present at any point in space where a moving charged particle feels a force. This describes the relationship between magnetic force and magnetic field. The unit of measurement of the magnetic field is the Tesla$\left(\mathrm{T}\right)$which is equivalent to Newtons per Ampere per metre$\left({\mathrm{NA}}^{-1}{\mathrm{m}}^{-1}\right)$.

Magnetic Poles

If you've ever played with bar magnets, you might have noticed that when you bring two faces of the magnets together, they will repel each other. If you flip one of the faces, the two faces near each other will attract each other. There is an evident push or pull between the faces, which indicates that some magnetic force exists between the magnets. Magnetic objects have two poles, or two ends, that will determine whether they will attract or repel other poles. These are called the north pole (N) and south pole (S) and are represented by the following figure of a typical bar magnet.

A typical bar magnet is shown in this image with north (N) and south (S) poles indicated. The north pole will attract the south pole of another magnet and vice-versa, Free SVG

The magnetic forces are determined as follows:

• like poles repel,
• unlike poles attract.

This explains the interactions we feel when we bring bar magnets close to each other. The region in which a magnetic pole of one magnet feels a magnetic force is within the magnetic field of the other magnet, and vice versa. We can think of a magnetic pole as producing magnetic fields as well and being affected by the magnetic fields of other magnetic poles.

Magnetic field lines

We may represent the lines along which the magnetic forces are acting with magnetic field lines, which we can see in the figure below. Magnetic field lines are not visible, instead, they are mathematical abstractions that contain information about how the magnetic field affects moving charge within its vicinity at every point in space; we only infer their presence by virtue of the force experienced by magnetic objects placed at each point in the field, and even then it is the force we measure not the magnetic field strength itself.

The magnetic field lines of a typical bar magnet indicated in this image tell us the direction of the force that would be exerted on a second north pole that enters this magnetic field, Wikimedia Commons CC BY-SA 4.0

The field lines start at the north pole and terminate on the south pole. The arrows show us the direction in which the north pole of a second magnet would feel a magnetic force if it enters the magnetic field of the first. It is clear to see that it would be repelled by the north pole and attracted towards the south pole of the first magnet. The closer the field lines are to each other, the stronger the magnetic field is, that is, the greater the magnetic force felt by another magnet.

Examples of magnetic field and force

We can use the depictions of the magnetic field lines for single magnets from before and try to imagine what the magnetic field lines would look like when two magnets are brought together in different orientations. Read through the two examples below and pay careful attention to the directions of the arrows in each case.

The formula relating magnetic force and magnetic field

We have seen the visual representation of the interaction between the magnetic fields of magnets, but our definition above extends to moving charges as well. That surely means that magnetic fields will interact with electric currents as well since an electric current is composed of moving charges. Let's assume a long, straight wire of length$L$is placed at right angles to a uniform magnetic field$B$. The wire is carrying a current$I$and will experience a force since the moving charges within the wire are exposed to this magnetic field. The force felt by the wire is given by the equation

$\begin{array}{rcl}\mathrm{Force}& =& \mathrm{magnetic}\mathrm{field}\mathrm{strength}\times \mathrm{current}\times \mathrm{length}\end{array}$

or in symbols,

$F=BIL$

The figure below illustrates this effect. A wire is placed perpendicular to a magnetic field between the poles of two magnets. The magnetic field points from left to right and the current points into the page. The wire feels a force that will push it downward. The downward direction can be obtained by applying Fleming's left-hand rule. Note that the wire can also be at any other angle other than 90° to the field (i.e. not perpendicular) but the calculation becomes a little more complicated and we will not deal with that scenario here.

A long, straight, current-carrying wire that is placed in a magnetic field will feel a force on it. This is due to the interaction between the field and moving charges in the wire, StudySmarter Originals

Differences between magnetic force and magnetic field

It is clear that the magnetic force and the magnetic field are two completely different quantities, even though they may appear similar. The table below lists three differences between the magnetic field and magnetic force on a charged particle at a point in the magnetic field.