clarification on an electric fields solution

Allenman

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

1. The problem statement, all variables and given/known data



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 = [itex]\frac{\kappa\lambda\delta l}{a^{2}}[/itex] = [itex]\frac{\kappa\lambda\delta\theta}{a}[/itex]

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

SammyS

It's because [itex]d\ell=a\cdot d\theta\,.[/itex]

Allenman

Does that come from the arc length formula?

Thank you

SammyS

Yes it does.