A Solenoid of Five Layers

Q. A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre, in teslas? expects 0.025 T

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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?

The playground

Inputs

length

L

80 cm

current

I

8 A

Outputs

field

B_{s}

The solution

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 Ruby

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

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

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

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)