A solenoid of radius 1.1 cm, carrying a current of 2.2 A, produces a magnetic field at its center of 0.28 T. How many turns per unit length does the solenoid have? A) 1.0 × 10⁵ m⁻¹ B) 1.0 × 10⁻⁹ m⁻¹ C) 1.1 × 10³ m⁻¹ D) 2.2 × 10³ m⁻¹ E) 7.0 × 10³ m⁻¹

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Quizplus · Accepted Answer

The magnetic field at the center of a solenoid is given by $B = \mu_0 n I$, where $B$ is the magnetic field, $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{Tm/A}$), $n$ is the number of turns per unit length, and $I$ is the current. Rearranging for $n$, we get $n = \frac{B}{\mu_0 I}$. Substituting the given values, $n = \frac{0.28}{4\pi \times 10^{-7} \times 2.2}$, which simplifies to approximately $1.0 \times 10^{5} \, \text{m}^{-1}$.

A Solenoid of Radius 1