Loop moving into a Constant Magnetic Field. Consider a square loop with side length 1m moving at a rate 0.1 m/s in the +x-direction into a magnetic field 6m long with constant strength and direction of B = 1 T 2 (into the page).

Loop moving into a Constant Magnetic Field. Consider a square loop with side length 1m moving at a rate 0.1 m/s in the +x-direction into a magnetic field 6m long with constant strength and direction of B = 1 T 2 (into the page).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Ferromagnetism

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Question

### Problem Statement:

**e. If the resistance of the loop is 2 ohms, calculate the induced current. Which way does it flow?**

### Explanation:

1. **Understanding the Problem:**
- We are given that the resistance of a loop is 2 ohms.
- We need to calculate the induced current in the loop.
- We also need to determine the direction of the induced current’s flow.

2. **Relevant Equations:**
- Ohm’s Law: \( I = \frac{V}{R} \), where \( I \) is the current, \( V \) is the voltage, and \( R \) is the resistance.
- Faraday’s Law of Induction, if additional information about the changing magnetic field is provided.

3. **Steps to Solve:**
- Determine the induced voltage (V) in the loop using Faraday's Law of Induction if the rate of change of magnetic flux is provided.
- Calculate the induced current using Ohm's Law: \( I = \frac{V}{R} \).
- Determine the direction of the current flow using Lenz’s Law, which states that the direction of the induced current opposes the change in magnetic flux.

### Notes:
- Ensure you have sufficient information regarding the magnetic flux change to compute the induced voltage.
- If the problem is theoretical, and only resistance is provided, additional details are required to fully solve for the current and its direction.

### Loop Moving into a Constant Magnetic Field

**Problem Statement:**

Consider a square loop with side length 1m moving at a rate of 0.1 m/s in the +x-direction into a magnetic field that is 6m long with a constant strength and direction of **B** = 1 T **ẑ** (into the page).

**Explanation:**

In this scenario, we have a square loop with each side measuring 1 meter. This loop is moving horizontally to the right (along the positive x-axis) at a speed of 0.1 meters per second into a region where a magnetic field exists. The magnetic field extends over a distance of 6 meters along the x-axis, and it has a uniform magnetic flux density of 1 Tesla directed into the page.

**Visual Representation:**
The description does not include a visual element, but you can imagine or sketch the following to aid understanding:
1. A square loop labeled with 1m sides.
2. An arrow showing the direction of movement of the loop to the right, labeled as 0.1 m/s.
3. A rectangular region of the magnetic field extending 6m in the x-direction, represented with dots or "X"s to denote the field pointing into the page.
4. An indication that the strength of the magnetic field within this region is 1 Tesla.

This setup can be used to analyze the behavior of the loop as it enters the magnetic field, which can lead to further discussions on concepts such as electromagnetic induction, Faraday's Law, and Lenz's Law.

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