(a) Suppose that the current in the solenoid is I(t). Within the solenoid, but far from its ends, what is the magnetic field B(t)) due to this current?(b) What is the magnetic flux Φ1(t) through a single turn of the solenoid?(c) Suppose that the current varies with time, so that dI(t)/dt≠0. Find the electromotive force EMF induced across the entire solenoid due to the change in current through the entire solenoid.(d) The self-inductance L is related to the self-induced EMF E(t) by the equation E(t)=−LdI(t)/dt. Find L for a long solenoid. (Hint: The self-inductance L will always be a positive quantity.) ### Air-Core Solenoid#### Diagram Explanation:1. **3D Illustration:** - The image shows an air-core solenoid, which is a coil of wire designed to create a magnetic field when an electric current passes through it. - The solenoid is oriented horizontally with the coil wrapping around a cylindrical form. - **Key Labels:** - **I**: Represents the electric current flowing through the solenoid from point A to point B. - **A and B**: Indicate the direction of the current entering and exiting the solenoid. - **R**: Denotes the radius of the solenoid's cylindrical shape. - **Z**: Represents the length of the solenoid. - \( \hat{z} \): Indicates the axis direction, aligning with the solenoid's length.2. **Schematic Symbol:** - Below the 3D illustration is the schematic symbol for a solenoid. - It consists of a series of loops representing the coiled wire. - The current \( I \) direction is shown entering at point A and exiting at point B, consistent with the 3D diagram.

Given:- The figure is given as Find:- (a) Suppose that the current in the solenoid is I(t). Within…

Answered: hat is the magnetic flux Φ1(t) through…

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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(a) Suppose that the current in the solenoid is I(t). Within the solenoid, but far from its ends, what is the magnetic field B(t)) due to this current?

(b) What is the magnetic flux Φ1(t) through a single turn of the solenoid?

(c) Suppose that the current varies with time, so that dI(t)/dt≠0. Find the electromotive force EMF induced across the entire solenoid due to the change in current through the entire solenoid.

(d) The self-inductance L is related to the self-induced EMF E(t) by the equation E(t)=−LdI(t)/dt. Find L for a long solenoid. (Hint: The self-inductance L will always be a positive quantity.)

### Air-Core Solenoid

#### Diagram Explanation:

1. **3D Illustration:**
- The image shows an air-core solenoid, which is a coil of wire designed to create a magnetic field when an electric current passes through it.
- The solenoid is oriented horizontally with the coil wrapping around a cylindrical form.
- **Key Labels:**
- **I**: Represents the electric current flowing through the solenoid from point A to point B.
- **A and B**: Indicate the direction of the current entering and exiting the solenoid.
- **R**: Denotes the radius of the solenoid's cylindrical shape.
- **Z**: Represents the length of the solenoid.
- \( \hat{z} \): Indicates the axis direction, aligning with the solenoid's length.

2. **Schematic Symbol:**
- Below the 3D illustration is the schematic symbol for a solenoid.
- It consists of a series of loops representing the coiled wire.
- The current \( I \) direction is shown entering at point A and exiting at point B, consistent with the 3D diagram.

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