A 12.9 cm long solenoid contains 817 turns and carries a current of 4.69 A. What is the strength B of the magnetic field at the center of this solenoid? B = T
A 12.9 cm long solenoid contains 817 turns and carries a current of 4.69 A. What is the strength B of the magnetic field at the center of this solenoid? B = T
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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![### Example Problem: Calculating the Magnetic Field Strength Inside a Solenoid
#### Problem Statement
A 12.9 cm long solenoid contains 817 turns and carries a current of 4.69 A. What is the strength \( B \) of the magnetic field at the center of this solenoid?
#### Solution
To calculate the magnetic field inside a solenoid, use 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 (in turns per meter),
- \( I \) is the current in amperes.
First, convert the length of the solenoid from centimeters to meters:
\[ \text{Length} = 12.9 \, \text{cm} = 0.129 \, \text{m} \]
Calculate \( n \) (number of turns per unit length):
\[ n = \frac{\text{Number of Turns}}{\text{Length}} = \frac{817}{0.129} \approx 6333.33 \, \text{turns/m} \]
Now, plug in the values into the formula:
\[ B = (4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}) \cdot (6333.33 \, \text{turns/m}) \cdot (4.69 \, \text{A}) \]
Calculate the product:
\[ B \approx 0.00374 \, \text{T} \]
So, the strength \( B \) of the magnetic field at the center of the solenoid is approximately 0.00374 T.
##### Final Answer
\[ B \approx 0.00374 \, \text{T} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e1db01-06d0-4e20-aae1-26f96b6814c3%2F474d644a-869f-419d-9125-4345b9093221%2Flvcp9n_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Problem: Calculating the Magnetic Field Strength Inside a Solenoid
#### Problem Statement
A 12.9 cm long solenoid contains 817 turns and carries a current of 4.69 A. What is the strength \( B \) of the magnetic field at the center of this solenoid?
#### Solution
To calculate the magnetic field inside a solenoid, use 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 (in turns per meter),
- \( I \) is the current in amperes.
First, convert the length of the solenoid from centimeters to meters:
\[ \text{Length} = 12.9 \, \text{cm} = 0.129 \, \text{m} \]
Calculate \( n \) (number of turns per unit length):
\[ n = \frac{\text{Number of Turns}}{\text{Length}} = \frac{817}{0.129} \approx 6333.33 \, \text{turns/m} \]
Now, plug in the values into the formula:
\[ B = (4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}) \cdot (6333.33 \, \text{turns/m}) \cdot (4.69 \, \text{A}) \]
Calculate the product:
\[ B \approx 0.00374 \, \text{T} \]
So, the strength \( B \) of the magnetic field at the center of the solenoid is approximately 0.00374 T.
##### Final Answer
\[ B \approx 0.00374 \, \text{T} \]
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