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Suppose that the electric potential varies along the x axis as shown in the graph. The potential does not vary in the y or z directions. V(volts) 15 |10 5 -3 -2 -1 2 -5 -10 а Of the intervals shown, determine the intervals in which the electric field has its largest and smallest magnitudes (i.e. the absolute value) and find those magnitudes. Ignore the behavior at the end points of the intervals. Emax Emin т

Suppose that the electric potential varies along the x axis as shown in the graph. The potential does not vary in the y or z directions. V(volts) 15 |10 5 -3 -2 -1 2 -5 -10 а Of the intervals shown, determine the intervals in which the electric field has its largest and smallest magnitudes (i.e. the absolute value) and find those magnitudes. Ignore the behavior at the end points of the intervals. Emax Emin т

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Electric Potential and Electric Field Analysis #### Overview The graph represents the variation of electric potential along the x-axis. The potential remains constant along the y and z directions. #### Graph Description - The vertical axis represents the electric potential \( V \) in volts. - The horizontal axis represents position along the x-axis. - Points of interest, labeled \( a \) through \( d \), indicate changes in potential. ##### Key Points on the Graph 1. **Point a (-3, -10)**: The potential starts at -10 volts. 2. **Point b (-2, 15)**: The potential quickly rises to 15 volts. 3. **Point c (0, 5)**: The potential decreases to 5 volts. 4. **Point d (2, 5)**: The potential remains constant at 5 volts. #### Task Determine the intervals where the electric field, derived from changes in potential, has the largest and smallest magnitudes. Calculate these magnitudes, disregarding endpoint behavior. #### Calculation Guidance The electric field \( E \) in a region where the potential changes linearly can be calculated by: \[ E = -\frac{\Delta V}{\Delta x} \] where \( \Delta V \) is the change in potential and \( \Delta x \) is the change in position. #### Input Area Calculate and enter the magnitudes of the electric field: - **Maximum Electric Field Magnitude \( E_{\text{max}} \):** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \left[ \frac{V}{m} \right] \) - **Minimum Electric Field Magnitude \( E_{\text{min}} \):** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \left[ \frac{V}{m} \right] \)
Transcribed Image Text:### Electric Potential and Electric Field Analysis #### Overview The graph represents the variation of electric potential along the x-axis. The potential remains constant along the y and z directions. #### Graph Description - The vertical axis represents the electric potential \( V \) in volts. - The horizontal axis represents position along the x-axis. - Points of interest, labeled \( a \) through \( d \), indicate changes in potential. ##### Key Points on the Graph 1. **Point a (-3, -10)**: The potential starts at -10 volts. 2. **Point b (-2, 15)**: The potential quickly rises to 15 volts. 3. **Point c (0, 5)**: The potential decreases to 5 volts. 4. **Point d (2, 5)**: The potential remains constant at 5 volts. #### Task Determine the intervals where the electric field, derived from changes in potential, has the largest and smallest magnitudes. Calculate these magnitudes, disregarding endpoint behavior. #### Calculation Guidance The electric field \( E \) in a region where the potential changes linearly can be calculated by: \[ E = -\frac{\Delta V}{\Delta x} \] where \( \Delta V \) is the change in potential and \( \Delta x \) is the change in position. #### Input Area Calculate and enter the magnitudes of the electric field: - **Maximum Electric Field Magnitude \( E_{\text{max}} \):** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \left[ \frac{V}{m} \right] \) - **Minimum Electric Field Magnitude \( E_{\text{min}} \):** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \left[ \frac{V}{m} \right] \)
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