Clarification on an electric fields solution

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

Homework Statement


physprob96.png



2. Solution given in solutions manual
physsol96.png



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

Homework Statement


physprob96.png


2. Solution given in solutions manual
physsol96.png


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...
It's because [itex]d\ell=a\cdot d\theta\,.[/itex]
 
Does that come from the arc length formula?

Thank you