- #1

SetepenSeth

- 16

- 0

## Homework Statement

Consider a conductor wire with a charge Q uniformly distributed, shaped in the form of an arc of radius R and amplitude 2A (were A is a given number between 0 and π).

Find the value of the electric field in the center of the arc.

## Homework Equations

##E(P)= \int K_e (dq/r^2)##

Where ##K_e## is the electrostatic constant[/B]

## The Attempt at a Solution

[/B]

Since the charge is uniformly distributed I'm considering the charge density as λ= Q/L thus Q= λL, where L = 2A. The point P is the center of the arc.

So the integral becomes

**##E(P)= \int K_e (λL/R^2)##**

Getting out the constants, integrating on dL and selecting the limits 0 - L=2A

##E(P)= K_e λ/R^2 \int_0^L LdL##

And solving:

##E(P)= 2A K_e λ / R^2##

However, if I leave it in terms of Q and Pi, the expression oversimplifies and the term 2A goes away

##E(P)= 2A Q / 4πε_0 R^2 2A ## ## =Q/4πε_0 R^2##

So I got the serious feeling I'm getting something wrong here. Perhaps integrate in terms of the angle?

Any advise would be appreciated