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title: "Two single-turn circular wire loops, Loop 1 and Loop 2, have identical loop radius and wire cross-sectional area. Loop 1 is made of a metal with resistivity \\(\\rho_0\\), and Loop 2 is made of a metal with resistivity \\(2\\rho_0\\). Both loops lie stationary in the plane of the page within a uniform magnetic field directed into the page whose magnitude varies with time according to \\(B(t) = \\beta t^2\\), where \\(\\beta\\) is a positive constant. At any time \\(t > 0\\), which of the following correctly compares the magnitude of the induced EMF \\(\\mathcal{E}\\) and the magnitude of the induced current \\(I\\) in the two loops?"
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url: "https://nerd-notes.com/ubq/121337/"
date_modified: "2026-08-23T04:59:47+00:00"
---

# Two single-turn circular wire loops, Loop 1 and Loop 2, have identical loop radius and wire cross-sectional area. Loop 1 is made of a metal with resistivity \(\rho_0\), and Loop 2 is made of a metal with resistivity \(2\rho_0\). Both loops lie stationary in the plane of the page within a uniform magnetic field directed into the page whose magnitude varies with time according to \(B(t) = \beta t^2\), where \(\beta\) is a positive constant. At any time \(t > 0\), which of the following correctly compares the magnitude of the induced EMF \(\mathcal{E}\) and the magnitude of the induced current \(I\) in the two loops?

Two single-turn circular wire loops, Loop 1 and Loop 2, have identical loop radius and wire cross-sectional area. Loop 1 is made of a metal with resistivity \(\rho_0\), and Loop 2 is made of a metal with resistivity \(2\rho_0\). Both loops lie stationary in the plane of the page within a uniform magnetic field directed into the page whose magnitude varies with time according to \(B(t) = \beta t^2\), where \(\beta\) is a positive constant. At any time \(t > 0\), which of the following correctly compares the magnitude of the induced EMF \(\mathcal{E}\) and the magnitude of the induced current \(I\) in the two loops?

![Two identical circular wire loops labeled Loop 1 on the left and Loop 2 on the right sit side by side in a single plane. Across the entire rectangular region, a regular array of six by four small 'x' marks indicates a uniform magnetic field \(\vec{B}(t)\) directed into the page. Below Loop 1 is the label \(\rho_1 = \rho_0\), and below Loop 2 is the label \(\rho_2 = 2\rho_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461187-hcxf4g.jpg)

- **A.** Induced EMF: \(\mathcal{E}_1 > \mathcal{E}_2\) Induced current: \(\mathcal{I}_1 > \mathcal{I}_2\)
- **B.** Induced EMF: \(\mathcal{E}_1 > \mathcal{E}_2\) Induced current: \(\mathcal{I}_1 = \mathcal{I}_2\)
- **C.** Induced EMF: \(\mathcal{E}_1 = \mathcal{E}_2\) Induced current: \(\mathcal{I}_1 > \mathcal{I}_2\)
- **D.** Induced EMF: \(\mathcal{E}_1 = \mathcal{E}_2\) Induced current: \(\mathcal{I}_1 = \mathcal{I}_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121337/*