A solenoid has 440 closely spaced turns, a length of 12.0 cm, a radius of 3.00 cm, and carries a current of 18.5 A. Determine the magnitude of the magnetic flux through the following.

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(a) the disk-shaped area of radius twice that of the solenoid that is perpendicular to and centered on the axis of the solenoid as shown in the figure
 
What is the definition of magnetic flux through a region? For this part, what is the magnitude of the magnetic field and what is the area over which there is a magnetic flux? Wb

(b) the annulus with an inner radius half that of the solenoid and an outer radius equal to that of the solenoid

What is the definition of magnetic flux through a region? For this part, what is the magnitude of the magnetic field and what is the area over which we are interested in the magnetic flux? Wb

### Solenoid Magnetic Flux Calculation

#### Problem Statement
A solenoid has the following specifications:
- **Number of closely spaced turns**: 440
- **Length**: 12.0 cm
- **Radius**: 3.00 cm
- **Current**: 18.5 A

Determine the magnitude of the magnetic flux through the specified regions.

#### Diagram Explanation
The diagram illustrates a solenoid aligned along the z-axis. It contains:
- A cylindrical shape representing the solenoid with marked dimensions.
- Several key points and regions labeled by their respective radii on the solenoid's surface:
  - **R/2**: Noted on the left half, indicating a radial slice in the solenoid.
  - **R**: Marked further along, showing the full radius.
  - **2R**: Positioned to indicate twice the full radius.

The diagram also includes axes:
- **x-axis**: Represented horizontally.
- **y-axis**: Represented vertically.
- **z-axis**: Aligned with the length of the solenoid, projecting outward in a 3D orientation.

#### Problem Requirements
Using the given data, calculate the magnetic flux, considering the magnetic field properties inside and any necessary formulas related to solenoids and magnetic fields.
Transcribed Image Text:### Solenoid Magnetic Flux Calculation #### Problem Statement A solenoid has the following specifications: - **Number of closely spaced turns**: 440 - **Length**: 12.0 cm - **Radius**: 3.00 cm - **Current**: 18.5 A Determine the magnitude of the magnetic flux through the specified regions. #### Diagram Explanation The diagram illustrates a solenoid aligned along the z-axis. It contains: - A cylindrical shape representing the solenoid with marked dimensions. - Several key points and regions labeled by their respective radii on the solenoid's surface: - **R/2**: Noted on the left half, indicating a radial slice in the solenoid. - **R**: Marked further along, showing the full radius. - **2R**: Positioned to indicate twice the full radius. The diagram also includes axes: - **x-axis**: Represented horizontally. - **y-axis**: Represented vertically. - **z-axis**: Aligned with the length of the solenoid, projecting outward in a 3D orientation. #### Problem Requirements Using the given data, calculate the magnetic flux, considering the magnetic field properties inside and any necessary formulas related to solenoids and magnetic fields.
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