### Problem StatementTwo 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.** \(\_\_\_\) mH2. **(b) What is the inductance of A?** \(\_\_\_\) mH3. **(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### ExplanationThis 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.

Given: The number of turns are N=320. The number of turns are N'=550. The current is I=3 A. The flux produced by A is ϕ=300 μWb. The flux produced by A is ϕ'=90 μWb. (a) The expression of mutual inductance is given by, M=N'ϕ'I Substitute the values in the above expression. M=550×90×10-6 Wb3 AM=0.0165 Wb/A×1 H1 Wb/AM=0.0165 H Thus, the mutual inductance of the solenoids is M=0.0165 H.(b) The expression to calculate the inductance is given by, L=NϕI Substitute the values in the above expression. L=320×300×10-6 Wb3 AL=0.032 Wb/A×1 H1 Wb/AL=0.032 H Thus, the mutual inductance of the solenoids is L=0.032 H.(c) Given: The rate of increase in current is dIdt=0.5 A/s. The emf induced in the B can be calculated as: e=M×dIdt Substitute the values in the above expression. e=0.0165 H×0.5 A/se=8.25×10-3 H·A/s×1 V1 H·A/se=8.25×10-3 Ve=8.25 mV Thus, the emf induced in the solenoid B is e=8.25 mV.

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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 uWb through each turn of A and a flux of 90.0 uwb through each turn of B. (a) Calculate the mutual inductance of the two solenoids. mH (b) What is the inductance of A? mH (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

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 uWb through each turn of A and a flux of 90.0 uwb through each turn of B. (a) Calculate the mutual inductance of the two solenoids. mH (b) What is the inductance of A? mH (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

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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