How Do You Calculate the Electric Field Ex at a Point in a Voltage Field?

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Discussion Overview

The discussion revolves around calculating the electric field component Ex at a specific point in a voltage field defined by the electric potential function V(x,y) = 20x^4 + 60y^3. Participants explore methods for deriving Ex using calculus, specifically focusing on the gradient and partial derivatives.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents a problem involving the electric potential function and seeks to calculate Ex at the point (2,1).
  • Another participant suggests using the negative gradient to find the electric field.
  • A follow-up question asks for clarification on how to apply the gradient method.
  • Participants discuss the formula for finding the gradient in rectangular coordinates.
  • It is proposed that to find Ex, one should take the partial derivative of the potential function with respect to x, resulting in 80x^3, while noting that the y term does not affect this calculation in this specific case.
  • There is a mention that the disappearance of y terms when taking the partial derivative with respect to x is not a general rule and may vary in other scenarios.

Areas of Agreement / Disagreement

Participants generally agree on the method of using partial derivatives to find Ex, but there is some uncertainty regarding the application of the gradient and the role of y in different contexts.

Contextual Notes

Participants express confusion about the calculus involved, particularly in deriving the electric field from the potential function, indicating a potential gap in understanding the application of partial derivatives and the gradient in this context.

wiiman3893
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Here is the problem:

Given that electric potential is given as a function of x and y: V(x,y)=20x4 + 60y3

What is Ex at (2,1)?

I have tried using E=-DV/DV, but I keep getting confused on how to derive this as it's been a while since I took calculus. I am also unsure of how to plug in the number, like if I only derive the x component and only plug the x into it, or if the y component is involved.
 
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Use the -gradient.
 
And how would I do that?
 
What's the formula for finding the gradient of a function in rectangular coordinates?
 
If using the gradient, just take the partial derivatives. One with respect to x, the other with respect to y.

If I understand the question right, you want to just take the partial derivative with respect to x to get Ex. That's 80x^3. The y term completely disappears.

In this particular example when you take the partial with respect to x, all of the y terms disappear. That doesn't always happen. So all you would have is plug in the 2 for x.
 
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