Magnetic Field Surrounding a Straight Conductor

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

For this problem,

Part of the solution is,

However, would someone please tell me where they got the sine function circled in red from?

Many thanks!

 

[TSny]

However, would someone please tell me where they got the sine function circled in red from?

You're working with the cross product $\vec{ds} \times \hat r$. How is the angle between $\vec{ds}$ and $\hat r$ related to the angle $\theta$ shown in diagram $a$?

 

[ChiralSuperfields]

You're working with the cross product $\vec{ds} \times \hat r$. How is the angle between $\vec{ds}$ and $\hat r$ related to the angle $\theta$ shown in diagram $a$?

Thank you @TSny ! I see how they got theta now. :) If we call the angle between ds and r hat as theta 2, then from the definition of the cross product:

dxsin(theta 2) = dxsin(pi/2 - theta) where I found theta 2 using angles in a triangle add up to 180 degrees.