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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Transcribed Image Text:A thin 12-cm-long solenoid has a total of 460 turns of wire and carries a current of 1.9 A.
![**Topic:** Calculating the Magnetic Field Inside a Solenoid
**Objective:** Learn how to calculate the magnetic field inside a solenoid, particularly near its center.
**Key Concept:**
A solenoid is a long coil of wire, and when an electric current passes through it, a magnetic field is generated inside the coil. This field is relatively uniform inside the solenoid, especially near the center.
**Formula Used:**
The magnetic field (B) inside a solenoid is given by the formula:
\[ B = \mu_0 \cdot n \cdot I \]
Where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A} \)),
- \( n \) is the number of turns per unit length of the solenoid,
- \( I \) is the current flowing through the solenoid.
**Steps to Calculate:**
1. **Identify the Variables:** Determine the number of turns per unit length (\( n \)) and the current (\( I \)) flowing through the solenoid.
2. **Apply the Formula:** Substitute the known values into the formula to calculate the magnetic field (\( B \)).
**Applications:**
Understanding how to calculate the magnetic field inside a solenoid is crucial in designing electromagnets, electrical engineering, and various applications in physics where controlled magnetic fields are required.
**Further Exploration:**
- Investigate how the length and diameter of the solenoid affect the field uniformity.
- Explore how the field strength changes at different points along the length of the solenoid.
This foundational knowledge will enable students to better understand electromagnetism's role in modern technology.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa451162e-14ac-4cfd-a2c6-1eae7f4a5f1a%2F854f6965-29e7-4083-abfc-9e6c23f1101f%2F9nvdpps_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic:** Calculating the Magnetic Field Inside a Solenoid
**Objective:** Learn how to calculate the magnetic field inside a solenoid, particularly near its center.
**Key Concept:**
A solenoid is a long coil of wire, and when an electric current passes through it, a magnetic field is generated inside the coil. This field is relatively uniform inside the solenoid, especially near the center.
**Formula Used:**
The magnetic field (B) inside a solenoid is given by the formula:
\[ B = \mu_0 \cdot n \cdot I \]
Where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A} \)),
- \( n \) is the number of turns per unit length of the solenoid,
- \( I \) is the current flowing through the solenoid.
**Steps to Calculate:**
1. **Identify the Variables:** Determine the number of turns per unit length (\( n \)) and the current (\( I \)) flowing through the solenoid.
2. **Apply the Formula:** Substitute the known values into the formula to calculate the magnetic field (\( B \)).
**Applications:**
Understanding how to calculate the magnetic field inside a solenoid is crucial in designing electromagnets, electrical engineering, and various applications in physics where controlled magnetic fields are required.
**Further Exploration:**
- Investigate how the length and diameter of the solenoid affect the field uniformity.
- Explore how the field strength changes at different points along the length of the solenoid.
This foundational knowledge will enable students to better understand electromagnetism's role in modern technology.
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