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4.36 For cach of the distributions of the electric potential V shown in Fig. P4.36, sketch the corresponding distribution of E (in all cases, the vertical axis is in volts and the horizontal axis is in meters).

4.36 For cach of the distributions of the electric potential V shown in Fig. P4.36, sketch the corresponding distribution of E (in all cases, the vertical axis is in volts and the horizontal axis is in meters).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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# Educational Resource: Exploring Electric Potential Distributions ## Problem 4.36 **Objective:** For each of the distributions of electric potential \( V \) shown in Figure P4.36, sketch the corresponding distribution of \( E \). In all cases, the vertical axis is in volts, and the horizontal axis is in meters. ### Figure P4.36: Electric Potential Distributions This figure consists of three graphs depicting different distributions of electric potential \( V \) as a function of position \( x \). #### (a) Graph Description - The graph illustrates a piecewise linear function. - Starting at \( V = 0 \) at \( x = 0 \), it increases steadily to \( V = 30 \) volts at \( x = 3 \). - It remains constant at \( V = 30 \) volts from \( x = 3 \) to \( x = 5 \). - Then, it decreases linearly to \( V = -30 \) volts at \( x = 11 \). - The potential rises back up to \( V = 0 \) volts by \( x = 16 \). #### (b) Graph Description - This graph shows a sinusoidal-like oscillation. - The potential oscillates between \( V = 4 \) volts and \( V = -4 \) volts. - Peaks occur roughly at \( x = 1.5, 4.5, 7.5, \) and \( 10.5 \) meters. - Zero crossings happen at \( x = 3, 6, 9, 12, \) and \( 15 \) meters. #### (c) Graph Description - The potential starts at \( V = 0 \) volts at \( x = 0 \) and decreases, reaching a minimum of approximately \( V = -4 \) volts at \( x = 3 \). - It then rises to a maximum of \( V = 4 \) volts at \( x = 9 \). - Finally, it decreases back toward \( V = 0 \) volts around \( x = 16 \). ### Notes for Visualization - Understanding the relationship between electric potential \( V \) and electric field \( E \) can be crucial. The electric field can be derived from the spatial derivative of the potential: \( E = -dV/dx \). - Pay attention to regions where the
Transcribed Image Text:# Educational Resource: Exploring Electric Potential Distributions ## Problem 4.36 **Objective:** For each of the distributions of electric potential \( V \) shown in Figure P4.36, sketch the corresponding distribution of \( E \). In all cases, the vertical axis is in volts, and the horizontal axis is in meters. ### Figure P4.36: Electric Potential Distributions This figure consists of three graphs depicting different distributions of electric potential \( V \) as a function of position \( x \). #### (a) Graph Description - The graph illustrates a piecewise linear function. - Starting at \( V = 0 \) at \( x = 0 \), it increases steadily to \( V = 30 \) volts at \( x = 3 \). - It remains constant at \( V = 30 \) volts from \( x = 3 \) to \( x = 5 \). - Then, it decreases linearly to \( V = -30 \) volts at \( x = 11 \). - The potential rises back up to \( V = 0 \) volts by \( x = 16 \). #### (b) Graph Description - This graph shows a sinusoidal-like oscillation. - The potential oscillates between \( V = 4 \) volts and \( V = -4 \) volts. - Peaks occur roughly at \( x = 1.5, 4.5, 7.5, \) and \( 10.5 \) meters. - Zero crossings happen at \( x = 3, 6, 9, 12, \) and \( 15 \) meters. #### (c) Graph Description - The potential starts at \( V = 0 \) volts at \( x = 0 \) and decreases, reaching a minimum of approximately \( V = -4 \) volts at \( x = 3 \). - It then rises to a maximum of \( V = 4 \) volts at \( x = 9 \). - Finally, it decreases back toward \( V = 0 \) volts around \( x = 16 \). ### Notes for Visualization - Understanding the relationship between electric potential \( V \) and electric field \( E \) can be crucial. The electric field can be derived from the spatial derivative of the potential: \( E = -dV/dx \). - Pay attention to regions where the
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