# Homework Help: Electrostatic Problem at point on a conical surface

1. Mar 22, 2015

### roam

1. The problem statement, all variables and given/known data
I am trying to understand a solved problem which is about finding electrostatic potential at point b of the following conical surface with a given surface charge:

I have attached the worked solutions to this post. In the solutions, I don't understand how they have got the expression:

$\bar{r}=\sqrt{h^2+r^2-\sqrt{2}hr}$

3. The attempt at a solution

I appreciate it if anyone could explain how this expression was obtained.

Looking at the expression it looks like Pythagoras was used here with $\bar{r}$ being the hypotenuse. But when the vertical side is $h$, how do we get $r^2-\sqrt{2}hr$ as the other side? I'm very confused here.

Any helps is greatly appreciated.

#### Attached Files:

• ###### solns.jpg
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2. Mar 22, 2015

### TSny

The triangle formed by $h$, $r$, and $\bar{r}$ is not a right triangle. Can you see how the law of cosines can be used to get the expression for $\bar{r}$?

Last edited: Mar 22, 2015
3. Mar 23, 2015

### roam

No, how can I use the law of cosines when the triangle is not a right angle? Should I be considering a different triangle? I really have no idea how the expression for $\bar{r}$ was obtained.

4. Mar 23, 2015

### BvU

express r in $\mathcal r$

5. Mar 23, 2015

### TSny

The law of cosines applies to all triangles, not just right triangles.

See http://www.mathsisfun.com/algebra/trig-cosine-law.html

6. Mar 23, 2015

### roam

Thank you so much BvU for the diagram. It makes perfect sense now.

Thank you Tsny, I really appreciate the link.