A Solenoid of Five Layers

solved MagneticFieldOfCurrents

Q. A closely wound solenoid 80 cm $L = 80$ cm long has 5 layers of windings of 400 turns each $N = 2000$ . The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A $I = 8.0$ A, estimate the magnitude of B inside the solenoid near its centre, in teslas?

Inputs

length

L

80 cm

current

I

8 A

Outputs

field

B_{s}

How it's solved

Solved with MagneticFieldOfCurrents

Given

$L = 80$ cm
$I = 8.0$ A
$N = 2000$ from “5 layers of windings of 400 turns each”

Find $B_{s}$ .

Working

$L = 80$ cm $= 0.8$ m
turns on each metre(solenoid) $n = \frac{N}{L}$
$n = \frac{2000}{0.8}$
$n = 2500$ m⁻¹
field inside a long solenoid(solenoid) $B_{s} = μ_{0} \cdot n \cdot I$
$B_{s} = 1.25663706 \times 10^{−6} \cdot 2500 \cdot 8$
$B_{s} = 0.02513$ T
$B_{s} \approx 0.025$ Tto 2 significant figures

Conclusion

Inside a long solenoid the field depends only on the turns on each metre and the current, not on how wide the solenoid is.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :a_solenoid_of_five_layers do4  kind :numerical5  describes "A closely wound solenoid %{length} long has 5 layers of windings of 400 turns each. The diameter of the " \6            "solenoid is 1.8 cm. If the current carried is %{current}, %{field}, in teslas?"7  given length: "80 cm"8  given current: "8.0 A"9  asks field: "estimate the magnitude of B inside the solenoid near its centre"10end

solution.rb

1require_relative "../questions/a_solenoid_of_five_layers"2require_relative "../science/moving_charges_and_magnetism/magnetic_field_of_currents"34solve :a_solenoid_of_five_layers, using: MagneticFieldOfCurrents do5  objects :solenoid67  take length: solenoid.length_of_the_coil8  take current: solenoid.current910  deduce_from "5 layers of windings of 400 turns each", solenoid.turns => 20001112  field = solenoid.field_inside13  answer field:, in: "T", figures: 21415  conclusion "Inside a long solenoid the field depends only on the turns on each metre and the current, not on " \16             "how wide the solenoid is."17end

playground.rb

1require_relative "../solutions/a_solenoid_of_five_layers"23play_with :a_solenoid_of_five_layers do4  title "A Solenoid of Five Layers"5end

The laws it drew on

quantity	written	units	within	from
pi	$π$	—	0 … ∞	MagneticFieldOfCurrents
permeability of free space	$μ_{0}$	N/A²	—	MagneticFieldOfCurrents
current	$I$	A	—	MagneticFieldOfCurrents
turns	$N$	—	—	MagneticFieldOfCurrents
radius	$R$	m	—	MagneticFieldOfCurrents
length of the coil	$L$	m	—	MagneticFieldOfCurrents
turns per length	$n$	m⁻¹	—	MagneticFieldOfCurrents
field at the centre	$B_{c}$	T	—	MagneticFieldOfCurrents
field inside	$B_{s}$	T	—	MagneticFieldOfCurrents
distance from the wire	$d$	m	—	MagneticFieldOfCurrents
field near a wire	$B_{w}$	T	—	MagneticFieldOfCurrents
field at the centre of ground	$B_{c,g}$	T	—
turns of ground	$N_{g}$	—	—
current of ground	$I_{g}$	A	—
radius of ground	$R_{g}$	m	—
field at the centre of solenoid	$B_{c}$	T	—
turns of solenoid	$N$	—	—
current of solenoid	$I$	A	—
radius of solenoid	$R$	m	—
turns per length of ground	$n_{g}$	m⁻¹	—
length of the coil of ground	$L_{g}$	m	—
turns per length of solenoid	$n$	m⁻¹	—
length of the coil of solenoid	$L$	m	—
field near a wire of ground	$B_{w,g}$	T	—
distance from the wire of ground	$d_{g}$	m	—
field near a wire of solenoid	$B_{w}$	T	—
distance from the wire of solenoid	$d$	m	—
field inside of ground	$B_{s,g}$	T	—
field inside of solenoid	$B_{s}$	T	—

B_{c,c} = \frac{μ_{0} \cdot N_{c} \cdot I_{c}}{2 \cdot R_{c}}

field at the centre of a coil

n_{c} = \frac{N_{c}}{L_{c}}

turns on each metre

B_{w,w} = \frac{μ_{0} \cdot I_{w}}{2 \cdot π \cdot d_{w}}

field near a long straight wire

B_{s,c} = μ_{0} \cdot n_{c} \cdot I_{c}

field inside a long solenoid

B_{c,g} = \frac{μ_{0} \cdot N_{g} \cdot I_{g}}{2 \cdot R_{g}}

field at the centre of a coil(ground)

B_{c} = \frac{μ_{0} \cdot N \cdot I}{2 \cdot R}

field at the centre of a coil(solenoid)

n_{g} = \frac{N_{g}}{L_{g}}

turns on each metre(ground)

n = \frac{N}{L}

turns on each metre(solenoid)

B_{w,g} = \frac{μ_{0} \cdot I_{g}}{2 \cdot π \cdot d_{g}}

field near a long straight wire(ground)

B_{w} = \frac{μ_{0} \cdot I}{2 \cdot π \cdot d}

field near a long straight wire(solenoid)

B_{s,g} = μ_{0} \cdot n_{g} \cdot I_{g}

field inside a long solenoid(ground)

B_{s} = μ_{0} \cdot n \cdot I

field inside a long solenoid(solenoid)