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

[wiiman3893]

Here is the problem:

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

What is E_x 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.

 

[Antiphon]

Use the -gradient.

 

[wiiman3893]

And how would I do that?

 

[Antiphon]

What's the formula for finding the gradient of a function in rectangular coordinates?

 

[spaderdabomb]

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.