Lorrain & Corson: Help with Derivation of Fig 18.9/7.20

[classy cal]

can someone help me with a derivation in L&C. I am wrestling with Figure 18.9 (Fig 7.20 in second edition) . In Equations 18.36 and 18.37 (7.99 and 7.100), the element dl is substituted with acos(phi)dphi and I cannot see how this is derived.

 

[Redbelly98]

Welcome to Physics Forums! I have the 2nd edition of this book.

dl has a magnitude of a dφ. Moreover, we are only interested in the y-component of A, hence the additional factor of cos(φ). (The book explains, between equations 7.99 and 7.100, why the x-component of A must be zero.)

 

[classy cal]

Many thanks Redbelly.