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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
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 \[ B \approx 0.00374 \, \text{T} \]
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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