Question

In the Ampere's Law derivation for a solenoid, why does side \(cd\) (lying outside the solenoid) contribute nothing to \(\oint \vec{B} \cdot d\vec{l}\)?

Options

• Because \(\vec{B}\) is perpendicular to \(d\vec{l}\) along that side

• Because the magnetic field outside the solenoid, \(B_{\text{outside}}\), is approximately zero

• Because no current flows outside the solenoid

• Because the length of side \(cd\) is negligibly small

Answer 1

Side \(cd\) lies outside the solenoid where the magnetic field \(B_{\text{outside}} \approx 0\) due to the cancellation of fields from adjacent turns. Therefore, \(\vec{B} \cdot d\vec{l} \approx 0\) along this side, and it contributes nothing to the line integral. This differs from sides \(bc\) and \(da\), where the contribution is zero due to perpendicularity.