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title: "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.  | Parameter | Loop 1 | Loop 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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url: "https://nerd-notes.com/ubq/123327/"
date_modified: "2026-09-28T11:58:09+00:00"
---

# 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.

| Parameter | Loop 1 | Loop 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?

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.

| Parameter | Loop 1 | Loop 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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596689-gfRzxk.jpg)

- **A.** | Induced emf: \(4\varepsilon_1\) | Induced current: \(I_1\) | Rate of energy dissipation: \(4P_1\) |
- **B.** | Induced emf: \(8\varepsilon_1\) | Induced current: \(2I_1\) | Rate of energy dissipation: \(8P_1\) |
- **C.** | Induced emf: \(8\varepsilon_1\) | Induced current: \(2I_1\) | Rate of energy dissipation: \(16P_1\) |
- **D.** | Induced emf: \(8\varepsilon_1\) | Induced current: \(4I_1\) | Rate of energy dissipation: \(32P_1\) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123327/*