The direction of a magnetic field at a given point in space is called the magnetic field direction or B⃗ a . The symbol for magnetic field direction is a single left-pointing arrow.
Magnetic fields are described using either orthogonal coordinates (no unit) or coordinate units (units of tesla, ampere per meter, or newtons per ampere). The latter is more useful for practical applications.
The coordinate units used to describe the magnetic field direction at a point in space depend on how the surrounding medium (such as air or a metal bar) influences the magnetic field at that point. This article will focus on the most general case: orthogonal coordinates in which the influence of the outside medium is negligible.
This article will explain how to determine the B⃗a at any given point in space.
Is B⃗ a the same as B⃗ b?
No, the two vectors can be in opposite directions, as in Figure 3. The magnitude of B⃗ a can also be either greater or less than that of B⃗ b.
The direction of B⃗ a can also be arbitrary, as in Figure 4. In this case, the field at point A is said to be free-field, or independent of any other field(s) at point A.
In some cases, such as in a vacuum inside a conducting box, the vector B⃗ a at point A can be chosen to equal zero. In this case the field at point A is said to be null-field.
These three cases—free-field, null-field, and opposite-direction—can all occur simultaneously at point A.
What is the relationship between B⃗ and H?
The magnetic field at any point in space is always oriented in a constant direction. At any given point in space, the magnetic field is always oriented in one of two directions: north or south.
The strength of the magnetic field at any given point in space is equivalent to how strong the force would be that would be applied to a wire placed in that field. The stronger the field, the stronger the force on the wire.
The direction of the magnetic field at a given point in space is always such that a compass placed at that point will register a north pole on the surface of the magnet. A compass needle will always rotate so that its north pole points toward this orientation.
When considering only one dimension, it is easiest to think about a vertical bar with a coil of wire inside it. When you place this inside a uniform magnetic field, one end of the bar will have a higher chance of hitting an electron than the other end. This end will have a north pole, and the other end will have a south pole.
What is the direction of H at point A?
The magnetic field at any given point is the sum of all the magnetic fields at that point. Imagine a line drawn from point A to infinity, where infinity is as far away as you can go.
The length of this line is its diameter, so imagine a circle with diameter equal to the length of the line from point A to infinity.
Inside this circle, where the surface is flat, imagine tiny little magnets pointing in all different directions, like little compass needles. The strength of each of these magnets is determined by the surrounding magnetic field at that location.
When you add up all these tiny magnets (using some math, of course), you get the larger diameter magnetic field at point A. The direction of this larger diameter magnetic field at point A is northwest.
How do I find the direction of H at point A?
You can find the direction of H at any point A by using what is known as the cross product. The cross product is a mathematical operation that gives you a new vector based on two other vectors.
You first need to define two vectors: one from point A to point B and one from point A to point C. You then need to find the magnitude of H at point A, and you need all three points to do this.
The cross product takes into account only the direction of one of the two given vectors, so you need to make sure that both have the same direction. You then multiply them and take the inverse cosine of that product to get your new vector.
What are some applications of geomagnetic fields?
Numerous technologies, devices, and systems rely on a variety of geomagnetic fields. Some of these include GPS, radio broadcast antennas, and diesel engine navigation.
GPS devices rely on the global geomagnetic field to determine your location. A GPS device first calculates its position using an internal geomagnetic field and then looks to the outside world for confirmation.
Radio broadcast antennas use the Earth’s magnetic field to orient its transmitted signal. Diesel engines use a compass heading from the internal geomagnetic field to determine which way to go.
These are just a few examples of how integral the geomagnetic field is to our modern technology. Without it, many systems would fail or be much more difficult to operate.
Summary
The magnetic field at a given point in space can take any direction, even north south. How the field changes in direction at a point is what determines the shape of the magnetic field at that point.
The four possible combinations of how the magnetic field changes in direction at a point are called quadrants. These quadrants are clockwise and counterclockwise rotation, expansion and contraction, and north-south reversal.
Magnetic fields can either be continuous or discrete. A discrete magnetic field is one that exists as individual points or bundles of energy; these are referred to as magnets. A continuous magnetic field is not associated with any physical material and exists only as a tendency or force.
This article will discuss how to determine the direction of the continuous magnetic field at a given point in space.
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