Definition of electric field dE due to a small charge dQ

[twotaileddemon]

Homework Statement

Hi...
How can one be sure that
$$d\textbf{E}=\frac{kdQ}{r^2}(\cos\theta \textbf{i} + \sin\theta \textbf{j})$$
Is true for a small charge dQ
Is there some derivation for this?

Homework Equations

The Attempt at a Solution

I have a problem for homework that uses this equation... I know how to solve the problem, but I feel like I should know how this equation works since I don't want to just mindlessly plug in information... Thanks.

 

[naresh]

A small enough charge dQ can be considered a point charge. The equation is just a statement of Coulomb's law.

$$d\textbf{E}=\frac{kdQ}{r^2}\hat{r}$$

The unit vector $$\hat{r}$$ in Cartesian coordinates gives you what you have.

 

[twotaileddemon]

A small enough charge dQ can be considered a point charge. The equation is just a statement of Coulomb's law.

$$d\textbf{E}=\frac{kdQ}{r^2}\hat{r}$$

The unit vector $$\hat{r}$$ in Cartesian coordinates gives you what you have.

Ohh okay I get it now, thanks. I understand where the sin and cosine come from now
:)
Thanks so much!