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Chapter 7, Problem 56P In a particular region, the electric potential is given by V = -xy²z + 4xy. What is the electric field in this region?

Chapter 7, Problem 56P In a particular region, the electric potential is given by V = -xy²z + 4xy. What is the electric field in this region?

College Physics
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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Under the calculation portion of the included images for Ez electric field portion why is it xy^2 and not xy^2+4xy?

[Chapter 7, Problem 56P In a particular region, the electric potential is given by V = -xy²z + 4xy . What is the electric field in this region? SAVE
Transcribed Image Text:[Chapter 7, Problem 56P In a particular region, the electric potential is given by V = -xy²z + 4xy . What is the electric field in this region? SAVE
To determine The equation of electric field from the equation of electric potential. Answer to Problem 56P Ē = (y²z + 4y) i + (2xyz + 4x) j + (xy²) k E Explanation of Solution Given: Equation of electric potential, V = -xy²z + 4xy Formula used: Electric field components Ꮩ Ꮩ -ov, E₁ = V₁ E₂ = - dv Ey Ez Əx dy дz Ex Calculation: Electric field components == Ex Ey Ez Conclusion: av dx av дz = a(-xy²z+4xy) dx a(-xy²z+4xy) dy a(-xy²z+4xy) dz = y²z + 4y = 2xyz + 4x = = xy² Electric field vector in that region E = (y²z + 4y) i + (2xyz + 4x)j + (xy²) k.
Transcribed Image Text:To determine The equation of electric field from the equation of electric potential. Answer to Problem 56P Ē = (y²z + 4y) i + (2xyz + 4x) j + (xy²) k E Explanation of Solution Given: Equation of electric potential, V = -xy²z + 4xy Formula used: Electric field components Ꮩ Ꮩ -ov, E₁ = V₁ E₂ = - dv Ey Ez Əx dy дz Ex Calculation: Electric field components == Ex Ey Ez Conclusion: av dx av дz = a(-xy²z+4xy) dx a(-xy²z+4xy) dy a(-xy²z+4xy) dz = y²z + 4y = 2xyz + 4x = = xy² Electric field vector in that region E = (y²z + 4y) i + (2xyz + 4x)j + (xy²) k.
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