In a certain region of space the electric potential is given by V=+Ax^2y−Bxy^2, where A= 5.00 V/m^3 and B= 8.00 V/m^3.Part A Calculate the magnitude of the electric field at the point in the region that has coordinates x= 1.10 m, y= 0.400 m, and z= 0. Express your answer to three significant figures and include the appropriate units.Part B Calculate the direction angle of the electric field at the point in the region that has coordinates x= 1.10 m, y= 0.400 m, and z= 0. Express your answer in degrees.∘, measured counterclockwise from the positive x-axis in the xy plane

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Asked Sep 21, 2019
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In a certain region of space the electric potential is given by V=+Ax^2y−Bxy^2, where A= 5.00 V/m^3 and B= 8.00 V/m^3.


Part A
Calculate the magnitude of the electric field at the point in the region that has coordinates x= 1.10 m, y= 0.400 m, and z= 0.
Express your answer to three significant figures and include the appropriate units.


Part B
Calculate the direction angle of the electric field at the point in the region that has coordinates x= 1.10 m, y= 0.400 m, and z= 0.
Express your answer in degrees.

∘, measured counterclockwise from the positive x-axis in the xy plane

 

 

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Expert Answer

Step 1

Given,

Electric potential v = Ax'y-Bxy
Where
A 5.00 V/m3 and B = 8.00 V/m3
So,
V = 5x2y-8xy
.1)
help_outline

Image Transcriptionclose

Electric potential v = Ax'y-Bxy Where A 5.00 V/m3 and B = 8.00 V/m3 So, V = 5x2y-8xy .1)

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Step 2

Part A: The magnitude of the electric field at the point in the region that has coordinates x = 1.1 m, y = 0.4 m, and z = 0.

Partially differentiate equation (1) with respect to x, y and z respectively:

EL
a(5xy-8xy2)
=10xy-8y
Put x1.10 m, y = 0.400 m, and z = 0.
-
10x1.1x0.4-8(0.4)
=3.12
ду
a(5x'y-8xy2)
5x-16
Put x1.1 m, y= 0.4 m, and z = 0.
-5x(1.1)16x.x 0.4
=-0.99
дv
Ez
a(5x'y-8xy2)
=0
help_outline

Image Transcriptionclose

EL a(5xy-8xy2) =10xy-8y Put x1.10 m, y = 0.400 m, and z = 0. - 10x1.1x0.4-8(0.4) =3.12 ду a(5x'y-8xy2) 5x-16 Put x1.1 m, y= 0.4 m, and z = 0. -5x(1.1)16x.x 0.4 =-0.99 дv Ez a(5x'y-8xy2) =0

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Step 3

Magnitude of the electric field:

...
|E2+EE
(3.12) +(-0.99) +0
2.95876
2.959 V/m
help_outline

Image Transcriptionclose

|E2+EE (3.12) +(-0.99) +0 2.95876 2.959 V/m

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