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| Both sides previous revision Previous revision Next revision | Previous revision | ||
| 184_notes:examples:week9_detecting_b [2021/07/01 15:12] – schram45 | 184_notes:examples:week9_detecting_b [2021/07/05 21:58] (current) – [Solution] schram45 | ||
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| ===Approximations & Assumptions=== | ===Approximations & Assumptions=== | ||
| - | | + | * We are only interested in the $B$-field at this specific moment in time: As the particle moves some its parameters may change (i.e. velocity, charge...). This assumption gives use fixed variables to work with at this snapshot in time, simplifying down the complexity of the model. |
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| ===Representations=== | ===Representations=== | ||
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| \vec{B}_3 &= \frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \vec{r}_3}{{r_3}^3} = 4.2 \text{ nT } \hat{z} | \vec{B}_3 &= \frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \vec{r}_3}{{r_3}^3} = 4.2 \text{ nT } \hat{z} | ||
| \end{align*} | \end{align*} | ||
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| + | Observation location 3 is the furthest away from our moving point charge and we would expect it to have a smaller magnetic field than location 2, this is reflected in our solution. We also expected the magnetic field at location 1 to be 0 since the velocity and separation vector are parallel for this point (this is always a good thing to look for when approaching a problem with cross products). | ||