# Differences

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184_notes:b_sup_comp [2021/06/16 15:09] bartonmo [How can we use a computer for this?] |
184_notes:b_sup_comp [2021/06/16 15:16] (current) bartonmo |
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While calculating the integral will give you an exact value for the magnetic field, it is possible to end up with an integral that is difficult or impossible to solve. Instead we can use the fact that the magnetic field obeys the principle of superposition to define a powerful algorithm for computing the magnetic field at any given location from any shape of current/ | While calculating the integral will give you an exact value for the magnetic field, it is possible to end up with an integral that is difficult or impossible to solve. Instead we can use the fact that the magnetic field obeys the principle of superposition to define a powerful algorithm for computing the magnetic field at any given location from any shape of current/ | ||

- | ==== The Superposition Principle ==== | + | ===== The Superposition Principle ===== |

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

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where $\vec{B}_1$ would be the magnetic field from one piece of the wire, $\vec{B}_2$ would be the magnetic field from a second piece of the wire, and so on. This idea of adding together the magnetic field from each chunk of the wire will form the basis of what we want the computer to calculate for us. | where $\vec{B}_1$ would be the magnetic field from one piece of the wire, $\vec{B}_2$ would be the magnetic field from a second piece of the wire, and so on. This idea of adding together the magnetic field from each chunk of the wire will form the basis of what we want the computer to calculate for us. | ||

- | ==== How can we use a computer for this? ==== | + | ===== How can we use a computer for this? ===== |

For most real-world situations, the magnetic field integral cannot be solved analytically. That is, you could most likely write down the integral, but it cannot be computed because there' | For most real-world situations, the magnetic field integral cannot be solved analytically. That is, you could most likely write down the integral, but it cannot be computed because there' |