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zimovet [89]
3 years ago
11

A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 4.5 A,

how many turns must the solenoid have?
Physics
1 answer:
daser333 [38]3 years ago
4 0

Answer:

<h2>16,931 turns</h2>

Explanation:

The magnetic field produced is expressed using the formula

B = \frac{\mu_0NI}{L}

B is the magnetic field = 0.30T

I is the current produced in the coil = 4.5A

\mu_0 is the magnetic permittivity in vacuum = 1.26*10^-6Tm/A

L is the length of the solenoid = 32 cm = 0.32 m

N is the number of turns in the solenoid.

Making N the subject of the formula from the equation above;

B = \frac{\mu_0NI}{L}\\\\BL = \mu_0NI\\\\Dividing\ both\ sides \ by \ \mu_0I\\\\\frac{BL}{\mu_0I} =\frac{\mu_oNI}{\mu_0I} \\\\

N = \frac{BL}{\mu_0I}

Substituting the give values to get N;

N = \frac{0.3*0.32}{1.26*10^{-6} * 4.5}\\\\N = \frac{0.096}{0.00000567} \\\\N = 16,931.21

The number of turns the solenoid must have is approximately 16,931 turns

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