A long straight wire carries a current I, as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it? Hig A I I I up I ---->>
A long straight wire carries a current I, as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it? Hig A I I I up I ---->>
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)...
Related questions
Question
![### Inducing a Counterclockwise Current in a Loop
**Problem Statement:**
A long straight wire carries a current \( I_0 \) as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it?
**Diagram Explanation:**
- A vertical line represents the long straight wire carrying current \( I_0 \).
- To the left of the wire, there is a horizontal dashed line indicating the direction in which the loop should be moved.
- An upward dotted arrow is shown next to the wire, labeled "up".
**Approach:**
To solve the problem, use the concept of electromagnetic induction (Faraday's Law) which states that a change in magnetic flux through a closed loop induces an electromotive force (EMF) around the loop. The direction of the induced current is given by Lenz's Law, which states that the induced current will flow in a direction such that it opposes the change in magnetic flux.
1. **Magnetic Field around the Wire:**
- The magnetic field (\( B \)) around a long straight current-carrying wire forms concentric circles with the wire at the center.
- By the right-hand rule, with the thumb pointing in the direction of the current (\( I_0 \)), the fingers curl around the wire in the direction of the magnetic field.
- For an upward current (\( I_0 \)), the magnetic field around the wire circulates counterclockwise when viewing the wire from above.
2. **Change in Magnetic Flux:**
- The loop needs to be moved in such a way that the magnetic flux through it changes.
- If the loop is moved to the left, towards the wire, the magnetic flux passing through the loop increases.
- If the loop is moved to the right, away from the wire, the magnetic flux through the loop decreases.
3. **Inducing Counterclockwise Current:**
- To induce a counterclockwise current in the loop (using Lenz's Law), the loop needs to be moved in such a direction that it opposes the increase in magnetic flux.
- Moving the loop to the right would decrease the magnetic flux through the loop because it moves away from the source of the magnetic field. This would induce a current in the loop that creates a magnetic field to oppose the decrease — in this case creating a magnetic field](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F83bd02c6-d02f-4764-a848-15fcab9c3f4f%2Fe7d4b3b6-d2e4-45bb-8822-1435b2b425f9%2Fz7ymz2l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Inducing a Counterclockwise Current in a Loop
**Problem Statement:**
A long straight wire carries a current \( I_0 \) as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it?
**Diagram Explanation:**
- A vertical line represents the long straight wire carrying current \( I_0 \).
- To the left of the wire, there is a horizontal dashed line indicating the direction in which the loop should be moved.
- An upward dotted arrow is shown next to the wire, labeled "up".
**Approach:**
To solve the problem, use the concept of electromagnetic induction (Faraday's Law) which states that a change in magnetic flux through a closed loop induces an electromotive force (EMF) around the loop. The direction of the induced current is given by Lenz's Law, which states that the induced current will flow in a direction such that it opposes the change in magnetic flux.
1. **Magnetic Field around the Wire:**
- The magnetic field (\( B \)) around a long straight current-carrying wire forms concentric circles with the wire at the center.
- By the right-hand rule, with the thumb pointing in the direction of the current (\( I_0 \)), the fingers curl around the wire in the direction of the magnetic field.
- For an upward current (\( I_0 \)), the magnetic field around the wire circulates counterclockwise when viewing the wire from above.
2. **Change in Magnetic Flux:**
- The loop needs to be moved in such a way that the magnetic flux through it changes.
- If the loop is moved to the left, towards the wire, the magnetic flux passing through the loop increases.
- If the loop is moved to the right, away from the wire, the magnetic flux through the loop decreases.
3. **Inducing Counterclockwise Current:**
- To induce a counterclockwise current in the loop (using Lenz's Law), the loop needs to be moved in such a direction that it opposes the increase in magnetic flux.
- Moving the loop to the right would decrease the magnetic flux through the loop because it moves away from the source of the magnetic field. This would induce a current in the loop that creates a magnetic field to oppose the decrease — in this case creating a magnetic field
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![Physics for Scientists and Engineers](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Lecture- Tutorials for Introductory Astronomy](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
![College Physics: A Strategic Approach (4th Editio…](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON