An ideal solenoid $20 \mathrm {~cm}$ long is wound with 5000 turns of very thin wire. What strength magnetic field is produced at the center of the solenoid when a current of $10 \mathrm {~A}$ flows through it? $\left( \mu _ { 0 } = 4 \pi \times \right.$ $\left. 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

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Quizplus · Accepted Answer

The magnetic field inside an ideal solenoid is given by $B = \mu_0 \frac{N}{L} I$, where $B$ is the magnetic field, $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{T} \cdot \text{m} / \text{A}$), $N$ is the number of turns, $L$ is the length of the solenoid in meters, and $I$ is the current in amperes. Substituting the given values: $B = 4\pi \times 10^{-7} \times \frac{5000}{0.2} \times 10 = 0.31 \, \text{T}$.

An Ideal Solenoid 20 cm20 \mathrm {~cm}20 cm Long Is Wound with 5000 Turns of Very Thin Wire

An Ideal Solenoid $20 \mathrm {~cm}$ Long Is Wound with 5000 Turns of Very Thin Wire