MHB Deriving Y-Component of Uniform Electric Rod | E=-▽V

[Quintessential]

This is essentially the problem.

And this is what I did.

Realizing the following:

E = -▽V

I simply took the derivative in regards to the vertical component, in this case "a".

So:

-dV/da [the above formulae]

And I got the following:

Κλl/(a sqrt(l^2+a^2))

Does that seem about right?

**Sorry, I have no idea on how to operate the sexy mathjax characters.

 

[I like Serena]

This is essentially the problem.

And this is what I did.

Realizing the following:

E = -▽V

I simply took the derivative in regards to the vertical component, in this case "a".

So:

-dV/da [the above formulae]

And I got the following:

Κλl/(a sqrt(l^2+a^2))

Does that seem about right?

**Sorry, I have no idea on how to operate the sexy mathjax characters.

Welcome to MHB, Quintessential! :)

Yep. That seems about right, although your constant looks a bit weird.

Anyway, since they are asking for the y component of the electric field at point P, I would write:

$$E_y = \frac{k_\ell Q}{y \sqrt{\ell^2 + y^2}}$$

(If you click Reply With Quote, you can see what the mathjax looks like. ;))