Question

Applying Ampere's Law to the rectangular loop around a solenoid, the line integral equals \(Bl\) and the enclosed current is \(nlI\). Which sequence of steps correctly yields the magnetic field inside?

Options

• \(Bl = \mu_0 \cdot nI\), therefore \(B = \frac{\mu_0 nI}{l}\)

• \(Bl = \mu_0 \cdot I\), therefore \(B = \frac{\mu_0 I}{l}\)

• \(Bl = \mu_0 \cdot nlI\), therefore \(B = \mu_0 nI\)

• \(Bl = \frac{\mu_0 nI}{2}\), therefore \(B = \frac{\mu_0 nI}{2l}\)

Answer 1

Applying Ampere's Law: \(\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}\). With \(\oint \vec{B} \cdot d\vec{l} = Bl\) and \(I_{\text{enc}} = nlI\), we get \(Bl = \mu_0 \cdot nlI\). Dividing both sides by \(l\) yields the standard result \(B = \mu_0 nI\).