184_notes:b_sup_comp

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184_notes:b_sup_comp [2018/03/06 19:11] – dmcpadden184_notes:b_sup_comp [2020/08/23 21:42] – dmcpadden
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 +/*[[184_notes:b_shapes|Next Page: Shapes of Wire and Magnetic Field]]
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 +[[184_notes:b_current|Previous Page: Currents Make Magnetic Fields]]*/
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 ===== Using Superposition of Magnetic Field and the Computer ===== ===== Using Superposition of Magnetic Field and the Computer =====
  
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 This equation tells us that if we split a line of current ($I$) into small chunks of length ($d\vec{l}$), we can calculate the magnetic field at an observation point from that chunk of length (using the $\vec{r}$). The integral then allows us to add the magnetic field from each little chunk to find the net magnetic field at the observation point. This equation tells us that if we split a line of current ($I$) into small chunks of length ($d\vec{l}$), we can calculate the magnetic field at an observation point from that chunk of length (using the $\vec{r}$). The integral then allows us to add the magnetic field from each little chunk to find the net magnetic field at the observation point.
  
-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/wire. In these notes, you will read about how you can structure code to calculate the magnetic field from any current source.+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/wire. This is very similar to what we did with the [[184_notes:comp_super|electric field from a line before]]. In these notes, you will read about how you can structure code to calculate the magnetic field from any shape of current-carrying wire.
  
 ==== The Superposition Principle ==== ==== The Superposition Principle ====
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 ==== 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's no anti-derivative for the function that you would be trying to integrate. So we have to think of another approach -- one that makes use of the principle of superposition, which we know the electric field obeys.+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's no anti-derivative for the function that you would be trying to integrate. So we have to think of another approach -- one that makes use of the principle of superposition, which we know the magnetic field obeys.
  
 Let's think through the process for computing the magnetic field due to the current in any kind of wire: Let's think through the process for computing the magnetic field due to the current in any kind of wire:
  • 184_notes/b_sup_comp.txt
  • Last modified: 2021/06/16 19:16
  • by bartonmo