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--- 184_notes:examples:week9_detecting_b [2018/07/03 03:52] – curdemma
+++ 184_notes:examples:week9_detecting_b [2021/07/05 21:58] (current) – [Solution] schram45
@@ Line 18: / Line 18: @@
 ===Approximations & Assumptions===
-  * The particle can be treated as a point particle..
+  * 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.
-  * We are only interested in the $B$-field at this specific moment in time.
 ===Representations===
   * We represent the Biot-Savart Law for magnetic field from a moving point charge as
 $$\vec{B}=\frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \vec{r}}{r^3}$$
+<WRAP TIP>
+===Approximation===
+We must approximate the particle as a point particle in order to use the magnetic field equation above. Since the problem doesn't say anything otherwise and it is a necessary approximation to solve the problem, this is an approximation we will make.
+</WRAP>
   * We represent the situation with diagram given above.
@@ Line 55: / Line 58: @@
 \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*}
+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).