# Magnetic Flux Density

Electric and magnetic fields are terms we often hear, but have you ever wondered how they are related? When we combine these two fields, we get an electromagnetic field. Electric and magnetic fields are interconnected, and together they make up the foundation of electromagnetism.

When an electric current flows through a system, it generates a magnetic field. The strength of this magnetic field is known as magnetic flux density. It's measured by the direction of the magnetic field acting on a certain region of space.

It's important to note that electric currents are the basic objects of magnetic interactions, just as electric charges are the basic objects for electric interactions. While there's much more to learn about Maxwell's laws and electromagnetism, understanding the relationship between electric and magnetic fields is a great first step.

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## How is magnetic flux density produced?

Let's take a look at an infinitely long straight wire that carries an electric current of intensity I. In this scenario, we'll explore two different settings that are often intertwined. Wires carrying electric current can create a magnetic flux density and be affected by electric fields, just like electric charges can create an electric field and be influenced by other electric fields.

**Generation of magnetic flux density with a wire**

To calculate the magnetic flux density created by our wire, we can use the following formula:

B = (μ0 * I) / (2π * r)

In this equation, vector B represents the magnetic flux density, r is the distance from the wire, vector ea is the vector twisting around the wire, and μ0 is the vacuum permeability with an approximate value of 1.⋅10-6.'s measured in Teslas (T), which is a unit defined as kg/s2 A, with A being amperes.

The image below shows the field lines for a wire, giving us a visual representation of the magnetic flux density created by the wire.

We are defining this field for an infinitely long wire, so it makes sense to consider quantities such as the magnetic flux density since we are only considering a quantity by area rather than a whole quantity defined on an infinite region.

**Experimental definition of magnetic flux density**

Let's consider the infinitely long wire with a current I again. This time we on presence a magnetic is by an external source and is constant in space, with a fixed value of B.

When we place the wire with the current under the influence of this magnetic flux density, a force will act on the wire in a similar way to how an electric field moves an electric charge. However, the rules for this interaction are more complex.

In general, magnetic fields behave perpendicular to electric fields. This can be seen in Figure 1, where the magnetic field is perfectly perpendicular to the direction of the current. This general feature translates to how magnetic fields affect currents.

To determine the direction in which a magnetic flux density affects a current, we need to use the "right-hand rule," as shown in the image below.

To summarize:

- Currents generate magnetic fields
- Magnetic flux density measures the strength of the magnetic field
- Magnetic fields can affect currents and wires through magnetic forces
- The force exerted by a magnetic field on a current is perpendicular to both the field and the current
- The right-hand rule can be used to determine the direction of the force
- The magnetic flux density is a vector field that does not exert a force in the direction to which it points, but rather in a direction perpendicular to it.

## Magnetic Flux Density

**What is magnetic flux density?**

It is the vector field measuring the strength of the magnetic field.

**How do we calculate magnetic flux density?**

For a wire carrying a current, one needs to take into account the radial distance to the wire and the intensity of the current. The formula is B = μ0·I/2·π·r.

**What is magnetic flux density measured in?**

It is measured in Teslas.

**Is magnetic flux density a vector?**

Yes, it has a spatial direction that does not signal the direction of the associated force.

**Why do we use magnetic flux density?**

Because it allows us to measure the strength of the magnetic field per unit of length, area, or volume. This is necessary because we usually deal with infinitely large objects for simplicity.