*Now that we got the basics down, let’s introduce a new term:*

- Magnetic Flux Density
- Tesla
- Measuring magnetic flux density

__What is magnetic flux density?__

## The **force** experienced per unit **length** by a straight conductor carrying unit **current** & placed at **right angles** to a magnetic field.

### It is represented by **B**.

This *official* definition relies on the **motor effect** explained here!

**Remember:**

F = BIL sin θ

So,

B = F/(IL sin θ)

If θ = 90°,

## B = F/IL

Magnetic flux density has units of the **Tesla (T).**

## 1 Tesla is the uniform magnetic flux which, when acting perpendicularly to a long straight wire carrying a current of 1 Ampere, causes a force per unit length of 1 Nm^{-1} on the conductor.

This is why we use B as a measure of how strong a magnetic field is.

- Large magnetic flux density = more force per length per current = stronger magnetic field
- Although it is defined by the force on a current-carrying conductor, B is also used to describe the force on a permanent magnet
- We can represent B using Field Lines: the closer together field lines are, the larger the magnetic flux density

In 3D (the complete picture) | |

In 2D (cross-section) | |

In 2D (side view) |

In these representation, B is represented by the DENSITY of LINES passing through a cross-sectional area. You can visualise this by counting the number of lines per unit area – this is why we name it flux *density*.

Low magnetic flux density | |

High magnetic flux density |

** How do you measure magnetic flux density?**There are 2 ways to practically do so:

Using a current balance | The wire is held perpendicular to the permanent magnetic field. When current is switched on, the reading on the balance (F) changes as a force is created between the wire & the magnet due to the motor effect. The current is varied. Values of F for each value of I are recorded. Graph of F against I is plotted. F = BIL Gradient of the graph gives BL. L of the wire passing through the magnetic field is be measured. Thus, B of this specific permanent magnet can be calculated. |

Using a Hall probe(a measurement device which uses the principal of Hall voltage) | Hall probe must first be calibrated to Earth’s magnetic field by rotating it until it reaches a maximum reading. This reading is noted, & the probe is rotated 180° until another maximum is reached. The difference between the 2 readings is calculated, & the Earth’s magnetic field is given by HALF of this difference. To measure B of a magnet, the Hall probe is held so that the field lines pass directly through it. To ensure accurate readings, the probe is rotated until a maximum is reached. |

*This concept of Magnetic Flux Density is often paired with a similar term: Magnetic Flux.*

*See here for an explanation on that.*

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