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184_notes:ind_graphs [2022/11/26 15:17] – valen176 | 184_notes:ind_graphs [2022/12/05 16:08] – valen176 | ||
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===== Induction Graphs ===== | ===== 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' |
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+ | $$V_{ind} = -\frac{d\Phi_b}{dt}$$ | ||
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+ | 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: | First let's consider when $\Phi_B$ rises and falls linearly with the same magnitude of slope: | ||
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[{{184_notes: | [{{184_notes: | ||
- | $\Phi_B(t)$ looks like a quadratic centered about t = 2. We can see that while $\Phi_B(t)$ is decreasing ($0< | + | $\Phi_B(t)$ looks like a quadratic centered about t = 2. We can see that while $\Phi_B(t)$ is decreasing ($0< |
Specifically, | Specifically, | ||
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$$\Phi_B(t) = (t-2)^2$$ | $$\Phi_B(t) = (t-2)^2$$ | ||
- | $$\frac{d \Phi_B}{dt} = 2(x-2)$$ | + | Taking a first derivative with respect to time yields: |
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+ | $$\frac{d \Phi_B}{dt} = 2(t-2)$$ | ||
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+ | Multiplying by $-1$ to find $V_{ind}$ gives: | ||
- | $$V_{ind} = -2(x-2)$$ | + | $$V_{ind} = -2(t-2)$$ |