Differences

This shows you the differences between two versions of the page.

--- 184_notes:ind_graphs [2022/11/26 15:17] – valen176
+++ 184_notes:ind_graphs [2022/12/05 16:08] – valen176
@@ Line 1: / Line 1: @@
 ===== Induction Graphs =====
-In these notes, we will examine a few examples of changing magnetic fluxes and associated induced voltages.
+In these notes, we will examine a few examples of changing magnetic fluxes and associated induced voltages. Recall from the previous notes that these are related by **Faraday's Law** which says:
+$$V_{ind} = -\frac{d\Phi_b}{dt}$$
+This is saying that the induced current is the **negative slope** of the magnetic flux.
 First let's consider when $\Phi_B$ rises and falls linearly with the same magnitude of slope:
@@ Line 45: / Line 49: @@
 [{{184_notes:examples:ind_graph3.png?800|  }}]
-$\Phi_B(t)$ looks like a quadratic centered about t = 2. We can see that while $\Phi_B(t)$ is decreasing ($0<t<2$), $V_{ind}$ is positive, and while $\Phi_B(t)$ is increasing ($2<t<8$), $V_{ind} is negative.
+$\Phi_B(t)$ looks like a quadratic centered about t = 2. We can see that while $\Phi_B(t)$ is decreasing ($0<t<2$), $V_{ind}$ is positive, and while $\Phi_B(t)$ is increasing ($2<t<8$), $V_{ind}$ is negative.
 Specifically, in this case we have:
@@ Line 51: / Line 55: @@
 $$\Phi_B(t) = (t-2)^2$$
-$$\frac{d \Phi_B}{dt} = 2(x-2)$$
+Taking a first derivative with respect to time yields:
+$$\frac{d \Phi_B}{dt} = 2(t-2)$$
+Multiplying by $-1$ to find $V_{ind}$ gives:
-$$V_{ind} = -2(x-2)$$
+$$V_{ind} = -2(t-2)$$