# Differences

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184_notes:b_summary [2020/08/23 18:22] dmcpadden |
184_notes:b_summary [2021/06/16 18:14] (current) bartonmo |
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It is an experimental fact that moving electric charges generate magnetic fields in all of space. When we observe a magnetic field, we know that is often due to some charge or collection of charges that are moving relative to our location in space (unless it’s due to a changing electric field as we will see soon). | It is an experimental fact that moving electric charges generate magnetic fields in all of space. When we observe a magnetic field, we know that is often due to some charge or collection of charges that are moving relative to our location in space (unless it’s due to a changing electric field as we will see soon). | ||

- | ==== Models of magnetic field ==== | + | ===== Models of Magnetic Field ===== |

The [[184_notes: | The [[184_notes: | ||

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This is called the Biot-Savart Law, but is really just an expression for superposition of the magnetic field. Later we will find that the pattern of the magnetic field in some cases suggests a short cut to finding the magnetic field that doesn’t involve superposition integrals. | This is called the Biot-Savart Law, but is really just an expression for superposition of the magnetic field. Later we will find that the pattern of the magnetic field in some cases suggests a short cut to finding the magnetic field that doesn’t involve superposition integrals. | ||

- | ==== Magnetic force ==== | + | ===== Magnetic Force ===== |

Magnetic fields can exert forces on moving charges, but these forces are always perpendicular to the motion of said charges. The [[184_notes: | Magnetic fields can exert forces on moving charges, but these forces are always perpendicular to the motion of said charges. The [[184_notes: | ||

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$$\vec{dF} = I d\vec{l} \times \vec{B} \longrightarrow \vec{F} = \int I d\vec{l} \times \vec{B}$$ | $$\vec{dF} = I d\vec{l} \times \vec{B} \longrightarrow \vec{F} = \int I d\vec{l} \times \vec{B}$$ | ||

- | Typically, the most common experience people have with magnetic force comes from permanent magnets, where the story is more complicated. We haven’t dived into the mathematical model for how forces in that situation work because while superposition continues to work, it means computing every magnetic field generated by every domain in one magnet and determining the force exerted on each domain of the other magnet and adding that all up! | + | Typically, the most common experience people have with magnetic force comes from permanent magnets, where the story is more complicated. We haven’t gotten into the mathematical model for how forces in that situation work because while superposition continues to work, it means computing every magnetic field generated by every domain in one magnet and determining the force exerted on each domain of the other magnet and adding that all up! |

- | ==== Work and Energy ==== | + | ===== Work and Energy ===== |

- | The definition of magnetic force shows us that [[184_notes: | + | The definition of magnetic force shows us that [[184_notes://**the force is always perpendicular to the motion, so magnetic fields can not do work!**// Magnetic forces are used to [[184_notes: |

However, this leads to a little bit of a difference between electric and magnetic fields, which is that there’s no such thing as a scalar magnetic potential (unlike [[184_notes: | However, this leads to a little bit of a difference between electric and magnetic fields, which is that there’s no such thing as a scalar magnetic potential (unlike [[184_notes: |