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184_notes:examples:week6_drift_speed [2017/09/26 15:56] – [Solution] tallpaul | 184_notes:examples:week6_drift_speed [2017/09/26 16:05] – [Solution] tallpaul | ||
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* Electron charge density for both wires. | * Electron charge density for both wires. | ||
* Electron current for both wires. | * Electron current for both wires. | ||
+ | * Cross-sectional area for both wires. | ||
===Approximations & Assumptions=== | ===Approximations & Assumptions=== | ||
Line 26: | Line 27: | ||
To find the cross-sectional area of the wire, we just use the area of a circle. We know the radius, so this should be easy: $A=\pi r^2$. | To find the cross-sectional area of the wire, we just use the area of a circle. We know the radius, so this should be easy: $A=\pi r^2$. | ||
+ | |||
+ | We are given current, and we can solve for electron current using the charge of an electron: $i = \frac{I}{q}$. | ||
+ | |||
+ | We now have enough information to solve for the drift speed of electrons. We use positive numbers below, since we care only about speed for now, not direction. | ||
+ | |||
+ | $$v_{avg} = \frac{I}{\pi r^2 n q}$$ | ||
+ | |||
+ | Current ($I$), radius ($r$), electron density ($n$), and electron charge ($q$) are all things we know for our two wires. When we plug in the numbers, we get the following: | ||
+ | \begin{align*} | ||
+ | v_{\text{avg, | ||
+ | \end{align*} |