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A solenoidal coil with 23 turns of wire is wound tightly around another coil with 340 turns. The inner solenoid is 22.0 cm long and has a diameter of 2.10 cm . At a certain time, the current in the inner solenoid is 0.100 A and is increasing at a rate of 1800 A/s.

A solenoidal coil with 23 turns of wire is wound tightly around another coil with 340 turns. The inner solenoid is 22.0 cm long and has a diameter of 2.10 cm . At a certain time, the current in the inner solenoid is 0.100 A and is increasing at a rate of 1800 A/s.

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
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### Transcription for Educational Website: --- **Understanding Electromagnetic Induction: A Practical Example** In this example, we explore the concept of electromagnetic induction using a solenoidal coil system. **Description of the System:** - **Inner Solenoid:** - Turns: 340 - Length: 22.0 cm - Diameter: 2.10 cm - **Outer Solenoid:** - Turns: 23 (wound tightly around the inner solenoid) At a given moment, the inner solenoid carries a current of 0.100 A. Additionally, this current is increasing at a rate of 1800 A/s. **Key Concepts:** Electromagnetic induction occurs when a change in current within a coil generates an electromotive force (EMF) in another nearby coil. This setup with two solenoids provides a practical demonstration of how changing magnetic fields induce currents in adjacent coils. Understanding these concepts is crucial for fields such as electrical engineering and physics, where electromagnetic principles are applied in designing motors, transformers, inductive sensors, and many other devices. --- **Explanation of Graphs/Diagrams:** There are no graphs or diagrams provided in this particular example. However, an associated diagram could typically illustrate: - The arrangement of the solenoids (one inside the other) - Direction of the current and how it changes over time - The magnetic field lines created by the inner solenoid - Induced EMF in the outer solenoid due to changing current in the inner solenoid. Such visual aids can significantly enhance understanding by providing a clear, visual representation of the concepts discussed.
Transcribed Image Text:### Transcription for Educational Website: --- **Understanding Electromagnetic Induction: A Practical Example** In this example, we explore the concept of electromagnetic induction using a solenoidal coil system. **Description of the System:** - **Inner Solenoid:** - Turns: 340 - Length: 22.0 cm - Diameter: 2.10 cm - **Outer Solenoid:** - Turns: 23 (wound tightly around the inner solenoid) At a given moment, the inner solenoid carries a current of 0.100 A. Additionally, this current is increasing at a rate of 1800 A/s. **Key Concepts:** Electromagnetic induction occurs when a change in current within a coil generates an electromotive force (EMF) in another nearby coil. This setup with two solenoids provides a practical demonstration of how changing magnetic fields induce currents in adjacent coils. Understanding these concepts is crucial for fields such as electrical engineering and physics, where electromagnetic principles are applied in designing motors, transformers, inductive sensors, and many other devices. --- **Explanation of Graphs/Diagrams:** There are no graphs or diagrams provided in this particular example. However, an associated diagram could typically illustrate: - The arrangement of the solenoids (one inside the other) - Direction of the current and how it changes over time - The magnetic field lines created by the inner solenoid - Induced EMF in the outer solenoid due to changing current in the inner solenoid. Such visual aids can significantly enhance understanding by providing a clear, visual representation of the concepts discussed.
### Inductance and Magnetic Flux Calculations #### Part A: Calculating the Average Magnetic Flux For this exercise, you need to calculate the average magnetic flux \((Φ_B)\) through each turn of the inner solenoid. Use the appropriate formula and given data to find \(Φ_B\). \[Φ_B = \quad \text{[Input box]} \quad \text{Wb}\] * **Units**: Weber (Wb) * **Submit**: After entering the value, click the "Submit" button. * **Request Answer**: If you need help, click "Request Answer". #### Part B: Calculating the Mutual Inductance For this part, calculate the mutual inductance \((M)\) of the two solenoids. Use the appropriate inductance formula and given data. \[ M = \quad \text{[Input box]} \quad \text{H}\] * **Units**: Henry (H) * **Submit**: After entering the value, click the "Submit" button. * **Request Answer**: If you need help, click "Request Answer". #### Part C: Calculating the Induced EMF In this section, calculate the electromotive force (emf) \((ε_2)\) induced in the outer solenoid by the changing current in the inner solenoid using Faraday's law of induction. \[ ε_2 = \quad \text{[Input box]} \quad \text{V}\] * **Units**: Volts (V) * **Submit**: After entering the value, click the "Submit" button. * **Request Answer**: If you need help, click "Request Answer". Each part of the problem involves understanding and applying principles from electromagnetism, specifically regarding magnetic flux, mutual inductance, and induced electromotive force. Make sure to review relevant formulas and concepts before attempting to solve these problems.
Transcribed Image Text:### Inductance and Magnetic Flux Calculations #### Part A: Calculating the Average Magnetic Flux For this exercise, you need to calculate the average magnetic flux \((Φ_B)\) through each turn of the inner solenoid. Use the appropriate formula and given data to find \(Φ_B\). \[Φ_B = \quad \text{[Input box]} \quad \text{Wb}\] * **Units**: Weber (Wb) * **Submit**: After entering the value, click the "Submit" button. * **Request Answer**: If you need help, click "Request Answer". #### Part B: Calculating the Mutual Inductance For this part, calculate the mutual inductance \((M)\) of the two solenoids. Use the appropriate inductance formula and given data. \[ M = \quad \text{[Input box]} \quad \text{H}\] * **Units**: Henry (H) * **Submit**: After entering the value, click the "Submit" button. * **Request Answer**: If you need help, click "Request Answer". #### Part C: Calculating the Induced EMF In this section, calculate the electromotive force (emf) \((ε_2)\) induced in the outer solenoid by the changing current in the inner solenoid using Faraday's law of induction. \[ ε_2 = \quad \text{[Input box]} \quad \text{V}\] * **Units**: Volts (V) * **Submit**: After entering the value, click the "Submit" button. * **Request Answer**: If you need help, click "Request Answer". Each part of the problem involves understanding and applying principles from electromagnetism, specifically regarding magnetic flux, mutual inductance, and induced electromotive force. Make sure to review relevant formulas and concepts before attempting to solve these problems.
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