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The electric potential in a region of space is V =( 110 ² 110 y²) V, where and y are in meters. You may want to review (Page 714). For help with math skills, you may want to review: Part A What is the strength of the electric field at (x, y) = (3.0m, 2.0m) ?

The electric potential in a region of space is V =( 110 ² 110 y²) V, where and y are in meters. You may want to review (Page 714). For help with math skills, you may want to review: Part A What is the strength of the electric field at (x, y) = (3.0m, 2.0m) ?

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The electric potential in a region of space is V =( 110 x²- 110 y²) V, where x and y are in meters. You may want to review (Page 714). For help with math skills, you may want to review: Part A What is the strength of the electric field at (x, y) = (3.0m, 2.0m) ?
Transcribed Image Text:The electric potential in a region of space is V =( 110 x²- 110 y²) V, where x and y are in meters. You may want to review (Page 714). For help with math skills, you may want to review: Part A What is the strength of the electric field at (x, y) = (3.0m, 2.0m) ?
Expert Solution
Step 1

Electric Field:

The electric field at a point (x0, y0) can be defined as the negative gradient of the electric potential function at that point. Mathematically,

E→(x0,y0)=-(∇V)(x0,y0)                      (1)

where V is the electric potential function and ∇ represents the gradient operator (for two-dimensional space) which is given as,

∇=i^∂∂x+j^∂∂y

where i^ and j^ are the unit vectors along the x and y directions respectively.

 

NOTE: Only S.I. unit is used in the given problem so they are avoided in calculation part.

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Follow-up Question

What is the direction of the electric field at (x,y)=(3.0m,2.0m)=(3.0m,2.0m)? Give the direction as an angle (in degrees) counterclockwise from the positive x-axis?

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