Electric Field Above the Center of a Circular Loop (Ring) - Griffiths Electrodynamics Problem 2.5

In this video I will solve problem 2.5 as it appears in the 4th edition of Griffith's Introduction to Electrodynamics. The problem states the following: Find the electric field a distance z above the center of a circular loop of radius r that carries a uniform line charge.

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Introducing the Problem
01:30 Finding the r vector
05:30 Plugging everything into E
08:20 Solving the Integral
13:30 Please support me on my Patreon!

[molokoobby]

let me just admit that your channel made me fall in love with this course

[neilmitra]

Excellent explanation! The vector r direction is a very important explanation here. Thank you so much!

[nooralemadi]

Thank you so much for this clear explanation.

[kevinowens]

I may have missed something but I heard you mention cylindrical coordinates put you never computed for the z axis. And I saw the variable z in the problem. Did I miss something?

[valeriadiaz]

You are doing God's work. Thank you so much!