---
title: "A group of students is investigating electromagnetic induction. They have a rectangular loop of wire with a single turn, having a known width \\(w\\) and length \\(L\\). The loop is securely mounted flat on top of a non-conducting dynamics cart that can roll along a horizontal track. A large permanent magnet assembly creates a uniform magnetic field of magnitude \\(B\\) directed vertically downward over a specific region of the track, as shown in Figure 1. The magnetic field outside this region is negligible. The students want to experimentally determine the magnitude of the magnetic field \\(B\\) by moving the cart into the field region.  The following equipment is available: – The cart with the wire loop, track, and magnet assembly – A motion detector with a computer interface – A voltage sensor with a computer interface – A stopwatch and a meterstick – Assorted connecting wires"
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url: "https://nerd-notes.com/ubq/117722/"
date_modified: "2026-08-04T07:54:02+00:00"
---

# A group of students is investigating electromagnetic induction. They have a rectangular loop of wire with a single turn, having a known width \(w\) and length \(L\). The loop is securely mounted flat on top of a non-conducting dynamics cart that can roll along a horizontal track. A large permanent magnet assembly creates a uniform magnetic field of magnitude \(B\) directed vertically downward over a specific region of the track, as shown in Figure 1. The magnetic field outside this region is negligible. The students want to experimentally determine the magnitude of the magnetic field \(B\) by moving the cart into the field region.

The following equipment is available:
– The cart with the wire loop, track, and magnet assembly
– A motion detector with a computer interface
– A voltage sensor with a computer interface
– A stopwatch and a meterstick
– Assorted connecting wires

A group of students is investigating electromagnetic induction. They have a rectangular loop of wire with a single turn, having a known width \(w\) and length \(L\). The loop is securely mounted flat on top of a non-conducting dynamics cart that can roll along a horizontal track. A large permanent magnet assembly creates a uniform magnetic field of magnitude \(B\) directed vertically downward over a specific region of the track, as shown in Figure 1. The magnetic field outside this region is negligible. The students want to experimentally determine the magnitude of the magnetic field \(B\) by moving the cart into the field region.

The following equipment is available:
- The cart with the wire loop, track, and magnet assembly
- A motion detector with a computer interface
- A voltage sensor with a computer interface
- A stopwatch and a meterstick
- Assorted connecting wires

![A 3D perspective line drawing of a rectangular dynamics cart on a straight horizontal track. On top of the cart is a flat rectangular wire loop. The side of the loop perpendicular to the track is labeled 'w', and the side parallel to the track is labeled 'L'. Two wires lead from the loop to a small rectangular box labeled 'Voltage Sensor'. A box labeled 'Motion Detector' sits at the far left end of the track, facing the cart. A region of the track to the right of the cart is shaded gray and filled with uniformly spaced 'x' marks indicating a magnetic field directed downward into the track. A large label 'B' points to this region. An arrow labeled 'v' points from the cart to the right, toward the magnetic field region. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830041-BIod7y.jpg)

**Part a)** **Describe** an experimental procedure the students could use to determine the relationship between the constant speed \(v\) of the cart as it enters the magnetic field and the maximum induced emf \(\varepsilon\) in the loop. Assume the students have already measured \(w\) and \(L\). In your description, include: - How the students will use the available equipment to measure the speed \(v\) and the induced emf \(\varepsilon\). - Steps taken to ensure the speed is constant as the loop enters the magnetic field. - How the students will reduce experimental error. *(3 points)*

**Part b)** The students successfully perform the experiment and collect the data shown in the table below for a loop with width \(w = 0.05 \text{ m}\) and length \(L = 0.10 \text{ m}\). | Speed \(v\) (\(\text{m/s}\)) | Induced emf \(\varepsilon\) (\(\text{V}\)) | | :---: | :---: | | \(0.20\) | \(0.011\) | | \(0.40\) | \(0.019\) | | \(0.60\) | \(0.031\) | | \(0.80\) | \(0.039\) | | \(1.00\) | \(0.052\) | *(4 points)*

**Part c)** As the front edge of the loop enters the downward magnetic field, an induced current flows through the loop. *(4 points)*

**Part d)** The students replace the original wire loop with a new loop of identical dimensions but made of a wire with significantly greater electrical resistance. They push the cart so it enters the magnetic field at the exact same constant speed \(v\) as in one of their original trials. *(4 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117722/*