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Tarik winds a small paper tube uniformly with 181 turns of thin wire to form a solenoid. The tube's diameter is 8.97 mm and its length is 2.17 cm. What is the inductance, in microhenrys, of Tarik's solenoid?

Answer :

Evaluating this equation will give us the value of the inductance in henries. [tex]L = (4\pi * 10^-7) * (181)^2 * A / l[/tex]

This equation will give us the value of the inductance in henries. To convert it to microhenries, we need to multiply the result by 10^6.

To calculate the inductance of Tarik's solenoid, we need to use the formula:

L = (μ₀ * N² * A) / l

Where:
L is the inductance,
μ₀ is the permeability of free space (4π x [tex]10^{-7}[/tex] H/m),
N is the number of turns of wire,
A is the cross-sectional area of the solenoid,
l is the length of the solenoid.

First, let's convert the given dimensions to meters:
The diameter of the tube is 8.97 mm, so the radius is half of that, which is 4.485 mm or 0.004485 m.
The length of the tube is 2.17 cm, which is 0.0217 m.

Now, let's calculate the cross-sectional area of the solenoid:
A = π * r²
A = 3.1415 *[tex](0.004485)^2[/tex]

Next, we need to find the number of turns of wire. Tarik wound the wire 181 times.

Finally, we can calculate the inductance:
L = [tex](4\pi * 10^{-7}) * (181)^2 * A / l[/tex]

Evaluating this equation will give us the value of the inductance in henries. To convert it to microhenries, we need to multiply the result by [tex]10^6.[/tex]

Learn more about inductance in henries:

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