Choosing Integrating constants for Electric Field

[Jen2114]

Homework Statement

A nonconducting disk of radius R has a uniform positive surface charge density sigma. Find the Electric field at a point along the axis of the disk at a distance x from its center. Assume that x is positive

Homework Equations

E=kq/r

The Attempt at a Solution

I know I'm suppose to find dEX for one ring and then integrate to find the field due to all the rings.
dEx= (k) (2πσrx)dr /(x^2 +r^2) ^3/2
Why should you integrate this component from 0 to R and not R to -R

 

[DEvens]

Where exactly is the part of the disk from r=0 to r=-R? That is, where are the negative radius locations?

By the way, it is not an integrating constant as you suggest in the title. This is a definite integral so there is no integrating constant.

 

[LittleMrsMonkey]

For any future reference,what you mean is called "interval of integration" and not constants.

 

[Jen2114]

Hi,
sorry you're right I should've said that I don't understand why the limits of integration are 0 to R and not -R to R. The center of the disk is located at (0,0) and so the negative radius is at (0,-R) and the positive is at (0,R). The radius of the first ring I'm integrating is r and so then I have to integrate for the entire disk.

 

[Jen2114]

For any future reference,what you mean is called "interval of integration" and not constants.

Thank you, I will be much more clear next time

 

[LittleMrsMonkey]

Think about it logically.You are integrating radially outwards from 0.

 

[Jen2114]

So dEx=(1/4πε)*((2πσrx)/(x^2+r^2)^3/2)) is the electric field component in the x direction and so when you integrate to obtain the electric field for all the small rings in the disk , you are working your way out towards R, the radius of the entire disk. So that's why you integrate from 0 to R and not -R to R?

 

[LittleMrsMonkey]

It's easy,see?
You've forgotten the dr in your formula.

 

[Jen2114]

Ahhh ok I see thanks. Yeah, super clear now. Thanks I'll add the dr. Thanks again!

 

[LittleMrsMonkey]

You're welcome.I'm studying for an E-M exam right now anyway,so it's good use of my time.