Calculus Practice Test 2026 | Exam Prep Questions And Answers

The magnetic field inside a long solenoid with N turns per unit length carrying current I is given by which expression?

B = mu0 N I B = mu0 N I^2 B = mu0 I / N B = mu0 N / I

Correct Answer:

B = mu0 N I

Explanation:

Ampere's law applied to an ideal long solenoid gives a uniform magnetic field inside and negligible field outside. If you draw a rectangular Amperian loop with a long side of length L along the solenoid’s axis, the line integral is essentially B times L inside (the outside contribution is zero). The current enclosed by the loop is the total current from all turns within length L, which is (turns per unit length) times L times the current per turn: N L I. Ampere’s law then reads B L = μ0 (N L I), so the magnetic field inside is B = μ0 N I. This shows the field grows linearly with both the current and the density of turns.

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