Have you ever wondered how a microwave oven works? You may be surprised to know that it functions using the same principles that allow magnets to attach themselves to your refrigerator. Did you know that undergoing an MRI scan with an exposed piercing can cause the piercing to be ripped off your skin? Ouch! These phenomena are all caused by magnetic forces and magnetic fields. These fields could be as small as the space surrounding your refrigerator magnet or as large as the earth (or even larger).
Before defining a magnetic force, we need to recall the general definition of force.
A force is any interaction between two objects that will cause a change in the motion of the objects that are interacting. Simply put, it is a push or pull between two objects.
So magnets can provide a push or a pull on each other and even on charged particles, which is the basis upon which the microwave oven was invented. Let's learn more.
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.
A magnetic force is the force felt by a charged particle (electron, proton, ion, etc.) when it moves through a magnetic field.
It is a force that only differs from other forces because it is generated by magnets. It is measured in Newtonslike 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 a region in space where a moving charge or permanent magnet feels a force.
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 Teslawhich is equivalent to Newtons per Ampere per metre.
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.
Magnetic objects always exist as dipoles; a magnet will always have a north and south pole. What happens then if we cut a bar magnet right at the centre that separates the north and south magnetic poles? The answer is that we now have two smaller magnets each with two of its own magnetic poles, as seen in the figure below.
A magnet that is cut into smaller pieces will form smaller magnets each with its own north and south poles, Wikimedia Commons CC BY-SA 4.0
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 north pole of one bar magnet is brought near the south pole of another bar magnet, with their end faces parallel. How can the magnetic field lines between the two unlike poles be represented?
The magnetic field line pattern can be seen in the figure below. Note that the magnetic field lines start at the north poles and end at the closer of the two south poles. The attractive magnetic force between the magnets is evident and the two magnets will move toward each other (as long as there are no other forces, such as friction).
This image shows the magnetic field lines between unlike poles of two bar magnets. The magnets attract each other and the direction of the field lines are different at different points, Wikimedia Commons CC BY-SA 3.0
The north pole of one bar magnet is brought near the north pole of another bar magnet, with their end faces parallel. How can the field lines between the two like poles be represented?
The magnetic field line pattern can be seen in the following figure. Note that the magnetic field lines start at the north poles and end at the closer of the two south poles. The repulsive magnetic force between the magnets is evident and the two magnets will move away from each other (as long as there are no other forces, such as friction).
This image shows the magnetic field lines between like poles of two bar magnets. The magnets repel each other and the direction of the field lines are different at different points, Wikimedia Commons CC BY-SA 3.0
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 lengthis placed at right angles to a uniform magnetic field. The wire is carrying a currentand 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
or in symbols,
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
A wire of lengthcarrying a current ofis placed perpendicular to a uniform magnetic field of strength. Calculate the magnetic force that is experienced by the wire.
Answer: Let's first to identify the quantities that we know the magnitudes of. The length of the wire, the current isand the magnetic field strength. We can now use the equation that relates the magnetic force to the magnetic field to find the force on the wire,
The wire experiences a force, due to the magnetic field, of.
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.
Magnetic Force | Magnetic Field |
| The magnetic force on the particle is the force on it due to its interaction with the magnetic field. | The magnetic field is the region surrounding the particle in which the magnetic force is felt. |
| The magnetic force on the particle is measured in Newtons. | The magnetic field strength around the particle is measured in Teslas. |
| The magnetic force exists since there is a charged particle in the field to "feel" the force. | The magnetic field would exist even if the particle were not there. |
Magnetic Forces and Fields - Key takeaways
- A magnetic force on an object is any force that is due to the interaction between it and a magnetic field.
- A magnetic field is a region in space where a moving charge or permanent magnet feels a force.
- All magnets must have a north and south pole.
- Magnetic forces exist between the poles of magnets; like poles repel and unlike poles attract.
- Magnetic field lines represent the direction in which a magnetic north pole would move in the field.
- Magnetic field lines start on north poles and end on south poles.
- The quantity "magnetic field strength" has the symboland is measured in units of Teslas.
- Moving charges feel a force when moving relative to a magnetic field.
- Fleming's left-hand rule can be used to find the direction of the force on a current-carrying wire in a magnetic field.
- Stationary particles do not feel magnetic forces in magnetic fields.
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