*A new field!*

- Magnetic Fields
- Magnetic Field Lines
- Force on a current-carrying conductor in a magnetic field
- F = BIL sin θ
- Force between parallel current-carrying conductors

__What is a magnetic field?__

A **region** of space where a **force** is exerted on a **magnetic pole** OR a **moving charge**.

*We know that every field is generated & affected by some property:*

Gravitational Fields | Generated by mass | Field strength is represented by g |

Electric Fields | Generated by electric charge (+ or -) | Field strength is represented by E |

So,

__How are magnetic fields generated?__

Unlike the fields we have seen before, there are 2 ways a magnetic field can be created:

By permanently magnetic materials | Ex: Iron, cobalt, nickel are magnetic due to their chemical structures Force acts from North to South |

By moving electric charges | Ex: Moving electrons, protons, α-particles, or current in a wire Force acts according to the right hand grip rule |

Although it seems strange that there are 2 unrelated reasons for a single force to appear, they are actually similar at the quantum level. I won’t get into that in this post, but you can check out these links to investigate why:

Just like other fields, magnetic fields describe how forces act on magnetic poles/moving charges.

__We should be familiar with the basic properties of magnetic force:__

- It effects 2 possible poles (North & South)
- Like poles repel
- Unlike poles attract

## The strength of a magnetic field is represented by **B**.

This value is more accurately known as **MAGNETIC FLUX DENSITY**, which I will cover in the next post.

We can represent magnetic fields via **Magnetic Field Lines.**

__Characteristics of field lines:__

By convention, arrows show the direction of forces acting on a North pole | Around permanent magnetic poles, lines always start at N & end at S: Around moving charges, lines always obey the right hand grip rule: |

They are always smooth curves which never touch or cross | |

Density of lines indicate strength of field Closer lines = stronger field | |

Neutral points exist where there are no field lines (forces cancel each other out, so there is no net force in that region) | The area between the 2 magnets has no field lines, so it is a neutral point. |

Remember that these diagrams only show a 2D CROSS SECTION of the actual field, which is 3D!

*Falstad.com has a beautiful applet for simulating 3D magnetic fields, check this out:*

*Let’s take a closer look at the*…

**Magnetic Force** (AKA Motor Effect)

If I place a small magnet in a large permanent magnetic field like this: It would experience a force like this: |

Simple enough?

However, remember that this force also effects MOVING CHARGES, in a different way.

If I place a STATIONARY positive test charge in a large permanent magnetic field like this: It would experience NO FORCE. |

If I place a positive test charge which is MOVING INTO THE PAGE in a large permanent magnetic field like this: It would experience a FORCE like this: |

The same goes for a current-carrying conductor placed like so: |

This effect has many names, from the Laplace Force to the Magnetic Force.

Here, I will refer to it as the **Motor Effect** (but check your syllabus to see what they prefer!).

** Where does the Motor Effect come from?**A common explanation is the superposition of magnetic fields:

If a permanent magnetic field & a magnetic field due to a wire look like this: | |

The superposition of the 2 fields looks like this: | As there are more field lines on 1 side of the conductor, a force is generated from this side to the side with less field lines. |

*The original uploader was Theresa knott at English Wikibooks., CC BY-SA 2.5 https://creativecommons.org/licenses/by-sa/2.5, via Wikimedia Commons*

__How can we calculate the force generated?__

## F = BIL sin θ

The direction of this force can be determined using Fleming’s Left Hand Rule*:

*There are different variants of this rule, use the one you’re most comfortable with!

*For those who are into maths, this means that the force F is the cross product of the electric force vector & the magnetic force vector:*

*F** = I L x B*

Read more on cross products at Maths Is Fun.

**This implies a few things:**

force on a current-carrying conductor is maximum when the wire is perpendicular to the magnetic field | force on a moving charge is maximum when the direction of motion is perpendicular to the magnetic field |

force on a current-carrying conductor is 0 when the wire is parallel to the magnetic field | force on a moving charge is 0 when the direction of motion is parallel to the magnetic field |

*So far we’ve looked at the:*

- force between 2 magnets
- force between a magnet & a current-carrying conductor

…but how about the:

**Force between 2 parallel conductors**

Once again, we can use the **principal of superposition** to explain this:

When both currents are in the same direction: | |

When the 2 currents are in opposite directions: |

*Images from S-Cool*

**But we can also use the Motor Effect to CALCULATE the force between 2 wires!**

Here’s our example setup: | |

We can treat 1 wire as a permanent magnet generating field lines into the page | There is a formula to calculate the magnetic field strength due to a wire, but it is not required for A-Levels. Read more about it here. |

We can treat the other wire as a current-carrying conductor in a permanent magnetic field & calculate the force it experiences | F = BIL sin θ Since θ = 90°, F = BIL |

We can do this in any order & get the same answer! | |

This works regardless of the magnitude of current in either wire | The force calculated will be the SAME for both wires! |

This works regardless of the direction of the current in either wire | If both currents flow in the same direction, the wires will be pushed closer together: If the 2 currents flow in opposite directions, the wires will be pushed apart: |

*MikeRun, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons*

**REMEMBER:**

- BOTH forces are EQUAL in magnitude & OPPOSITE in direction (Newton’s 3
^{rd}Law) - the force ‘between’ the 2 wires is NOT the sum of the 2 forces, it is EQUAL to the 2 forces

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