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AP Physics 2
12.4 Electromagnetic Induction and Faraday’s Law
IntermediateMCQMathematicalProportional AnalysisConceptual20.2k
A grayscale schematic showing two side-by-side circular loops labeled Loop 1 on the left and Loop 2 on the right. Loop 1 is drawn as a circle of radius \(r_0\) lying in the plane of the page, surrounded by a rectangular boundary containing a uniform grid of four rows and four columns of dots representing a perpendicular magnetic field \(\vec{B}_1\). A straight arrow labeled \(r_0\) extends from the center of Loop 1 to its perimeter. Loop 2 is drawn as a larger circle of radius \(2r_0\) lying in the plane of the page, surrounded by a rectangular boundary containing a uniform grid of six rows and six columns of dots representing a perpendicular magnetic field \(\vec{B}_2\). A straight arrow labeled \(2r_0\) extends from the center of Loop 2 to its perimeter. No other labels, lines, text, or axes appear.
Two circular wire loops in perpendicular changing magnetic fields.
A student performs an experiment using two flat circular wire loops, Loop 1 and Loop 2, each placed in a region of uniform magnetic field directed perpendicularly to the plane of the loop. In each region, the magnitude of the magnetic field increases at a constant rate. The parameters for each loop and its corresponding magnetic field are summarized in the table.

ParameterLoop 1Loop 2
Rate of magnetic field change\(\Delta B / \Delta t\)\(2(\Delta B / \Delta t)\)
Loop radius\(r_0\)\(2r_0\)
Loop resistance\(R_0\)\(4R_0\)

If Loop 1 has an induced electromotive force \(\varepsilon_1\), an induced current \(I_1\), and a rate of thermal energy dissipation \(P_1\), which row in the table correctly identifies the induced electromotive force \(\varepsilon_2\), induced current \(I_2\), and rate of thermal energy dissipation \(P_2\) in Loop 2?

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