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Chapter 20: Problem 22

Verify that, in SI units, \(\Delta \Phi_{\mathrm{B}} / \Delta t\) can be measured in volts - in other words, that $1 \mathrm{Wb} / \mathrm{s}=1 \mathrm{V}$

Short Answer

Expert verified
Question: Verify that the rate of change of magnetic flux can be measured in volts, specifically that 1 Wb/s = 1 V. Answer: Following Faraday's law of electromagnetic induction and comparing the units of voltage with magnetic flux and time, we have verified that the rate of change of magnetic flux (1 Wb/s) is equivalent to 1 V in SI units.

Step by step solution

01

Write the definition of a volt in terms of electromotive force (EMF)

According to Faraday's law of electromagnetic induction, the electromotive force (EMF) induced in a circuit is directly proportional to the rate of change of magnetic flux through the circuit. Mathematically, it is represented by: $$\varepsilon = -\frac{\Delta \Phi_{\mathrm{B}}}{\Delta t}$$ Where \(\varepsilon\) is EMF, \(\Delta \Phi_{\mathrm{B}}\) is the change in magnetic flux, \(\Delta t\) is the change in time, and the negative sign indicates the direction of the induced EMF according to Lenz's law.
02

Define the units of measurements involved in the formula

We are given that magnetic flux \(\Phi_{\mathrm{B}}\) is measured in Weber (Wb) and time \(t\) is measured in seconds (s). The unit for EMF or voltage (V) is volts.
03

Compare the units of the formula with SI units of volts

From the formula derived in Step 1, we can write the units of voltage in terms of magnetic flux and time: $$1\mathrm{V} = \frac{1\mathrm{Wb}}{1\mathrm{s}}$$ This relation shows that the rate of change of magnetic flux \(1\mathrm{Wb} / \mathrm{s}\) is equivalent to \(1\mathrm{V}\) in SI units.
04

Conclusion

We have successfully verified that, in SI units, the rate of change of magnetic flux \(\Delta \Phi_{\mathrm{B}} / \Delta t\) can be measured in volts, or in other words, that \(1 \mathrm{Wb} / \mathrm{s} = 1 \mathrm{V}\).

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