College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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### Problem Statement

Two solenoids A and B, spaced close to each other and sharing the same cylindrical axis, have **320** and **550** turns, respectively. A current of **3.00 A** in solenoid A produces an average flux of **300 μWb** through each turn of A and a flux of **90.0 μWb** through each turn of B.

1. **(a) Calculate the mutual inductance of the two solenoids.**

   \(\_\_\_\) mH

2. **(b) What is the inductance of A?**

   \(\_\_\_\) mH

3. **(c) What is the magnitude of the emf that is induced in B when the current in A changes at the rate of **0.500 A/s**?**

   \(\_\_\_\) mV

### Explanation

This exercise involves calculating mutual inductance, inductance, and electromotive force (emf) using the properties of coupled solenoids. 

1. **Mutual Inductance Calculation:**
   - Formula: \( M = N_B \times \Phi_B / I \)
   - Where \( N_B \) is the number of turns in solenoid B, \( \Phi_B \) is the magnetic flux through B, and \( I \) is the current in solenoid A.

2. **Inductance of Solenoid A:**
   - Formula: \( L_A = N_A \times \Phi_A / I \)
   - Where \( N_A \) is the number of turns in solenoid A and \( \Phi_A \) is the magnetic flux through A.

3. **Induced emf in B:**
   - Formula: \( \text{emf} = -M \times (dI/dt) \)
   - Where \( dI/dt \) is the rate of change of current in solenoid A.

This information would be valuable for anyone studying electromagnetic induction and the properties of solenoids in electrical circuits.
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Transcribed Image Text:### Problem Statement Two solenoids A and B, spaced close to each other and sharing the same cylindrical axis, have **320** and **550** turns, respectively. A current of **3.00 A** in solenoid A produces an average flux of **300 μWb** through each turn of A and a flux of **90.0 μWb** through each turn of B. 1. **(a) Calculate the mutual inductance of the two solenoids.** \(\_\_\_\) mH 2. **(b) What is the inductance of A?** \(\_\_\_\) mH 3. **(c) What is the magnitude of the emf that is induced in B when the current in A changes at the rate of **0.500 A/s**?** \(\_\_\_\) mV ### Explanation This exercise involves calculating mutual inductance, inductance, and electromotive force (emf) using the properties of coupled solenoids. 1. **Mutual Inductance Calculation:** - Formula: \( M = N_B \times \Phi_B / I \) - Where \( N_B \) is the number of turns in solenoid B, \( \Phi_B \) is the magnetic flux through B, and \( I \) is the current in solenoid A. 2. **Inductance of Solenoid A:** - Formula: \( L_A = N_A \times \Phi_A / I \) - Where \( N_A \) is the number of turns in solenoid A and \( \Phi_A \) is the magnetic flux through A. 3. **Induced emf in B:** - Formula: \( \text{emf} = -M \times (dI/dt) \) - Where \( dI/dt \) is the rate of change of current in solenoid A. This information would be valuable for anyone studying electromagnetic induction and the properties of solenoids in electrical circuits.
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