Which expression gives the magnetic field inside a long solenoid with current I and turns per length N/L?

Which expression gives the magnetic field inside a long solenoid with current I and turns per length N/L?

• A. B = μ0 I / (N/L)
• B. B = μ0 I (N/L)
• C. B = μ0 (N/L) / I
• D. B = μ0 / (I (N/L))

Answer: (B)

The magnetic field inside a long solenoid is determined by how many turns there are per unit length and by the current flowing through those turns. For an ideal long solenoid, the field is uniform inside and given by B = μ0 n I, where n is the turns per unit length. Here n is N/L, so the field becomes B = μ0 I (N/L). This shows the field strengthens with both increasing current and increasing turn density. The other forms would imply the field either decreases with current or inversely with turn density, which contradicts the established relation that more turns per length and a larger current both raise the internal magnetic field.

The magnetic field inside a long solenoid is determined by how many turns there are per unit length and by the current flowing through those turns. For an ideal long solenoid, the field is uniform inside and given by B = μ0 n I, where n is the turns per unit length. Here n is N/L, so the field becomes B = μ0 I (N/L). This shows the field strengthens with both increasing current and increasing turn density. The other forms would imply the field either decreases with current or inversely with turn density, which contradicts the established relation that more turns per length and a larger current both raise the internal magnetic field.