A solenoid is created by wrapping a L = 55 m long wire around a hollow tube of diameter D = 4.5 cm. The wire diameter is d = 0.55 mm. The solenoid wire is then connected to a power supply so that a current of I = 8.5 A flows through the wire.

A. Write an expression for the number of turns, N, in the solenoid. You do not need to take into account the diameter of the wire in this calculation.

B. Calculate the number of turns, N, in the solenoid.

C. Write an expression for the length of the solenoid, (L2), in terms of the hollow tube D, the length of the wire L, and the diameter of the wire d. Assume it is constructed by using only 1 layer of loops (note that most solenoids are actually constructed using many layers to maximize magnetic field density).

D. Calculate the length of the solenoid, (L2), in meters.

E. Calculate the magnitude of the magnetic field at the center of the solenoid, in Tesla.

Since, there is only one layer of loop. Therefore, the length of solenoid can be easily found out by adding the diameter of wire for each turn. Hence:

L₂ = DN

where,

L₂ = Length of the solenoid

D = diameter of wire

N = No. of Turns

D.

using values in the equation we get:

L₂ = (0.045 m)(389)

L₂ = 17.5 m

E.

The magnitude of magnetic field inside solenoid is given by the formula:

B = μ₀NI/L₂

where,

B = Magnetic field inside solenoid

μ₀ = permeability = 4π x 10⁻⁷ T/A.m

I = current = 8.5 A

Therefore,

B = (4π x 10⁻⁷ T/A.m)(389)(8.5 A)/17.5 m)

B = 2.3 x 10⁻⁴ Web

oeerivona oeerivona · Answer 2 · 2022-02-16T20:37:51+01:00

The wire length, and the hollow tube diameter determines the number

of turns, which then gives the solenoid's length and magnetic field.

Responses:

[tex]A. \hspace{0.15 cm}The \ expression \ for \ the \ number \ of \ turns \ is; N = \underline{ \dfrac{L}{\pi \cdot D}}[/tex]

B. 389 (approximate value)

[tex]C. \hspace{0.15 cm}L_2 = d \times \left( \dfrac{L}{\pi \cdot D} \right)[/tex]

D. 0.21395 m

E. 1.94 × 10⁻² T

Which methods are used to evaluate a solenoid?

A. The number of turns in a solenoid, N, is given by the formula;

L = N × Circumference of the hollow tube

Which gives;

L = N × π·D

Therefore;

[tex]The \ number \ of \ turns, \ N = \underline{ \dfrac{L}{\pi \cdot D}}[/tex]

B. L = 55 m

D = 4.5 cm = 0.045 m

Which gives;

[tex]The \ number \ of \ turns \ in \ the \ solenoid,\ N = \dfrac{55 \, m}{\pi \times 0.045 \, m} \approx \underline{389 \ turns}[/tex]

C. The length of the solenoid, L₂, is given by the formula;

L₂ = d × N

Which gives;

[tex]\underline{L_2 =d \times \left( \dfrac{L}{\pi \cdot D} \right)}[/tex]

D. d = 0.55 mm = 0.00055 m

The length of the solenoid is therefore;

The length of the solenoid, L₂ ≈ 0.00055 m × 389 = 0.21395 m

E. The magnitude of the magnetic field at the center of the solenoid, B,

is given by the formula;

[tex]B = \mathbf{\dfrac{\mu_0 \cdot N \cdot I}{L_2}}[/tex]

Where;

μ₀ = Permeability of vacuum = 4·π × 10⁻⁷ T m/A

Which gives;

[tex]B \approx \mathbf{ \dfrac{4 \cdot \pi \times 10^{-7} \, T \cdot m/A\times 389 \times 8.5 \, A}{0.21395 \, m} } \approx 1.94 \times 10^{-2} \, T\alpha[/tex]

The magnitude of the magnetic field at the center, B ≈ 1.94 × 10⁻² T

Learn more about magnetic field strength here:

https://brainly.com/question/2605182