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A single loop of wire with an area of 0.0900 $\mathrm{m}^{2}$ is in a uniform magnetic field that has an initial value of 3.80 $\mathrm{T}$ , is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 $\mathrm{T} / \mathrm{s}$ . (a) What emf is induced in this loop? (b) If the loop has a resistance of $0.600 \Omega,$ find the current induced in the loop.

$$\begin{array}{l}{\text { a) } 0.0171 V} \\ {\text { b) } I=0.0285 A}\end{array}$$

Physics 102 Electricity and Magnetism

Chapter 21

Electromagnetic Induction

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Inductance

Alternating Current

Cornell University

Hope College

McMaster University

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so here for party to find the IMF. This is going to be equal to the change in magnetic flux with respect to time. And we know that the magnetic flux is equaling the magnetic field times the area times co sign of Fei and we know that fi is 90 degrees zero degrees rather so this will be equal to one. And the only thing changing here is the magnetic field. So the IMF is going to be equal to the area times the change in magnetic field with respect to time and this is going to be equal to 0.90 meters squared the area times 0.190 Tesla's per second. And so we find that the IMF is equal in point 0171 vault. Now, at this point, they want us to find the current. We know that according tto arms law, the voltage equals the current times, the resistance rather so this will be answered party to find the current however we need to his own law. So the voltage is equal to the current times the resistance and in this case it will equal the IMF so we can say that the current will simply be equal to the IMF, the Varda brother resistance. And so I will be in some part B. I will be equal to 0.171 and then this will be divided by their resistance of 0.600 comes and this is equaling Teo current of 0.0 285 amperes. So this would be your answer for party for part B brother, that is the end of the solution. Thank you for washing.

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