Clarification on an electric fields solution

[Allenman]

This isn't actually a homework problem. I just had a question about the solution they provided.

Homework Statement

2. Solution given in solutions manual

3. My question

When they convert dE into cylindrical coordinates why does the radius "a" lose its exponent?

dE = \frac{\kappa\lambda\delta l}{a^{2}} = \frac{\kappa\lambda\delta\theta}{a}

I have to be missing something simple, I just know it...

 

[SammyS]

This isn't actually a homework problem. I just had a question about the solution they provided.

Homework Statement

2. Solution given in solutions manual

3. My question

When they convert dE into cylindrical coordinates why does the radius "a" lose its exponent?

dE = \frac{\kappa\lambda\delta l}{a^{2}} = \frac{\kappa\lambda\delta\theta}{a}

I have to be missing something simple, I just know it...

It's because d\ell=a\cdot d\theta\,.

 

[Allenman]

Does that come from the arc length formula?

Thank you

 

[SammyS]

Yes it does.