The inductance of a solenoid that is $16.0 \mathrm {~cm}$ long and has a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ is $1.00 \mathrm { mH }$. How many turns of wire does this solenoid have? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$
A) 159,000
B) 318,000
C) 282
D) 1130
E) 150

Question

Quizplus · Accepted Answer

The inductance $L$ of a solenoid is given by $L = \mu_0 N^2 A / l$, where $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{T} \cdot \text{m} / \text{A}$), $N$ is the number of turns, $A$ is the cross-sectional area ($1.00 \times 10^{-4} \, \text{m}^2$), and $l$ is the length of the solenoid ($16.0 \, \text{cm} = 0.16 \, \text{m}$). Rearranging for $N$ and substituting the given values, we can solve for the number of turns.

The Inductance of a Solenoid That Is 16.0 cm16.0 \mathrm {~cm}16.0 cm Long and Has a Cross-Sectional Area Of

The Inductance of a Solenoid That Is $16.0 \mathrm {~cm}$ Long and Has a Cross-Sectional Area Of