What is the self-inductance of an ideal solenoid that is $300 \mathrm {~cm}$ long with a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ and has 1000 turns of wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$
A) $41.9 \mathrm { nH }$
B) $4.19 \mathrm { pH }$
C) $41.9 \mu \mathrm { H }$
D) $4.19 \mu \mathrm { H }$
E) $4.19 \mathrm { nH }$

Question

Quizplus · Accepted Answer

The self-inductance $L$ of an ideal solenoid is given by the formula $L = \mu_0 N^2 A / l$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$, $N = 1000$ turns, $A = 1.00 \times 10^{-4} \, \text{m}^2$, and $l = 300 \, \text{cm} = 3 \, \text{m}$. Substituting these values, $L = (4\pi \times 10^{-7}) \times (1000)^2 \times (1.00 \times 10^{-4}) / 3 = 41.9 \times 10^{-6} \, \text{H} = 41.9 \, \mu\text{H}$.

What Is the Self-Inductance of an Ideal Solenoid That Is 300 cm300 \mathrm {~cm}300 cm

What Is the Self-Inductance of an Ideal Solenoid That Is $300 \mathrm {~cm}$