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- Homework Statement
- Problem 2.5 from Griffiths EM:

Find Electric Field at a distance z above center of s circular loop of radius r that carries uniform line charge λ

- Relevant Equations
- E= ##frac{1/4πϵ} * ( \int {1/r^2} ) \hat r \ dq##

Hi.

I have solved the problem below as shown in the attached image. However I'm at a loss to figure out where I am making a mistake, and I know it is indeed a big goof up. Requesting guidance over identification and rectification of this big goof up.

(Edit- I can solve this problem in the component form by formulating that only vertical components remain while all horizontal ones are canceled by each other. My aim is to solve this problem in the generic ##\vec r## & ##\hat r## style which is used by Griffiths in his Examples for Chapter 2 to achieve the same result wrt vertical components)

I have solved the problem below as shown in the attached image. However I'm at a loss to figure out where I am making a mistake, and I know it is indeed a big goof up. Requesting guidance over identification and rectification of this big goof up.

(Edit- I can solve this problem in the component form by formulating that only vertical components remain while all horizontal ones are canceled by each other. My aim is to solve this problem in the generic ##\vec r## & ##\hat r## style which is used by Griffiths in his Examples for Chapter 2 to achieve the same result wrt vertical components)

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