Two long, straight, parallel wires carry steady currents \(I_1\) and \(I_2\) perpendicular to the \(xy\)-plane. An arbitrary closed Amperian loop \(C\) in the \(xy\)-plane encloses wire 1 but does not enclose wire 2. A student calculates the line integral around loop \(C\) and finds \(\oint_C \vec{B} \cdot d\vec{\ell} = \mu_0 I_1\). Which of the following best explains why current \(I_2\) does not affect the value of this line integral, and how \(I_2\) relates to the total magnetic field \(\vec{B}\) along path \(C\)?