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 56PIn a particular region, the electric potential is given by V = -xy²z + 4xy . What is the electric field in thisregion?SAVE To determineThe equation of electric field from the equation of electric potential.Answer to Problem 56PĒ = (y²z + 4y) i + (2xyz + 4x) j + (xy²) kEExplanation of SolutionGiven:Equation of electric potential, V = -xy²z + 4xyFormula used:Electric field componentsᏙᏙ-ov, E₁ = V₁ E₂ = - dvEyEzƏxdyдzExCalculation:Electric field components==ExEyEzConclusion:avdxavдz=a(-xy²z+4xy)dxa(-xy²z+4xy)dya(-xy²z+4xy)dz= y²z + 4y=2xyz + 4x== xy²Electric field vector in that region E=(y²z + 4y) i + (2xyz + 4x)j + (xy²) k.

Answered: Image /qna-images/answer/80dd4642-e777-4f33-9e64-11cf81edfdd3.jpg

Answered: Chapter 7, Problem 56P In a particular…

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?

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter7: Electric Potential

Section: Chapter Questions

Problem 56P: In a particular region, the electric potential is given by V=xy2z+4xy . What is the electric field...

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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

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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