What is the Potential Difference in a Non-Uniform Electric Field?

AI Thread Summary
The electric field in the problem is non-uniform, with Ex = (4.00 N/C·m) x and Ey = Ez = 0. To find the potential difference VB - VA, the integral Vb - Vi = -∫ba E * dS must be used, but the simple formula ΔV = Ed is not applicable due to the non-uniformity of the field. The correct potential difference calculated is -18V, which arises from integrating along a suitable path between the two points on different axes. The significance of the y-coordinate at point A is also discussed in relation to the integration process. Understanding the nature of the electric field is crucial for accurately determining potential differences in such scenarios.
PhysicsInNJ
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Homework Statement


The electric field in a region of space has the components Ey = Ez = 0 and Ex = (4.00 N/C·m) x. Point A is on the y axis at y = 3.60 m, and Point B is on thex axis at x = 3.00 m. What is the potential difference VB − VA?

Homework Equations


Vb- Vi = -∫ba E * dS

The Attempt at a Solution


The integral should become E*d, or 4*0.6 , but that is incorrect
The correct answer is -18V
 
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PhysicsInNJ said:

The Attempt at a Solution


The integral should become E*d, or 4*0.6 , but that is incorrect
The correct answer is -18V
Where does the 0.6 come from? Note that the two points are on different axes.
 
What's a good choice of path integration? Does the datum y = 3.6, as opposed to some other y number, have any significance?
 
PhysicsInNJ said:
The integral should become E*d
In addition to what the others said, ##\Delta V = Ed## only holds for uniform fields. You don't have a uniform field in this problem.
 

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