A graph of the electric field between two capacitor plates as a function of distance from the left plate is shown below. The distance between the plates is d, the direction of the field is to the right, and a battery is connected to the plates. 1. Which plate carries a positive charge?2. How many slabs of material have been inserted between the plates? What is the thickness of the material in terms of d?3. What can you say about the slab(s) inserted?4. Sketch a graph of the electric field between the plates when the slabs between the plates are removed and the battery remains connected. Useful information:C=QV=κC0Cplates=ϵ0AdCspheres=4πϵ0R1R2R2−R1Ccylinder=2πϵ0lln⁡(R2/R1) The image displays a graph illustrating the electric field strength \( E \) (in Newtons per Coulomb, N/C) as a function of position \( x \). The graph is characterized by a series of uniform rectangular waveforms.### Key Features of the Graph:1. **Axes**: - The horizontal axis represents the position \( x \). - The vertical axis represents the electric field strength \( E \) in units of N/C.2. **Waveform Characteristics**: - The electric field fluctuates between 0 and 5000 N/C. - The waveform consists of alternating horizontal lines and vertical jumps, creating a series of rectangles.3. **Intervals**: - Each interval on the horizontal axis is labeled as \(\frac{d}{5}\), \( \frac{2d}{5} \), \( \frac{3d}{5} \), \( \frac{4d}{5} \), and \( d \), indicating divisions of the distance \( d \) into five equal parts. - The electric field is constant at 5000 N/C for every segment between these intervals, followed by a drop to 0 N/C before rising back to 5000 N/C at the start of the next segment.4. **Pattern**: - The pattern is a repeating cycle of a step increase to 5000 N/C, a level segment, and a step decrease back to 0 N/C.This type of graph can represent a situation where the electric field strength is constant over certain regions, such as in specific configurations of electric charges or fields in segmented media.

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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

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A graph of the electric field between two capacitor plates as a function of distance from the left plate is shown below. The distance between the plates is d, the direction of the field is to the right, and a battery is connected to the plates.

1. Which plate carries a positive charge?

2. How many slabs of material have been inserted between the plates? What is the thickness of the material in terms of d?

3. What can you say about the slab(s) inserted?

4. Sketch a graph of the electric field between the plates when the slabs between the plates are removed and the battery remains connected.

Useful information:

C=QV=κC0

Cplates=ϵ0Ad

Cspheres=4πϵ0R1R2R2−R1

Ccylinder=2πϵ0lln⁡(R2/R1)

The image displays a graph illustrating the electric field strength \( E \) (in Newtons per Coulomb, N/C) as a function of position \( x \). The graph is characterized by a series of uniform rectangular waveforms.

### Key Features of the Graph:

1. **Axes**:
- The horizontal axis represents the position \( x \).
- The vertical axis represents the electric field strength \( E \) in units of N/C.

2. **Waveform Characteristics**:
- The electric field fluctuates between 0 and 5000 N/C.
- The waveform consists of alternating horizontal lines and vertical jumps, creating a series of rectangles.

3. **Intervals**:
- Each interval on the horizontal axis is labeled as \(\frac{d}{5}\), \( \frac{2d}{5} \), \( \frac{3d}{5} \), \( \frac{4d}{5} \), and \( d \), indicating divisions of the distance \( d \) into five equal parts.
- The electric field is constant at 5000 N/C for every segment between these intervals, followed by a drop to 0 N/C before rising back to 5000 N/C at the start of the next segment.

4. **Pattern**:
- The pattern is a repeating cycle of a step increase to 5000 N/C, a level segment, and a step decrease back to 0 N/C.

This type of graph can represent a situation where the electric field strength is constant over certain regions, such as in specific configurations of electric charges or fields in segmented media.

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