Inside a Solenoid

solved MagneticFieldOfCurrents

Q. A solenoid of length 0.5 m $L = 0.5$ m has a radius of 1 cm and is made up of 500 $N = 500$ turns. It carries a current of 5 A $I = 5$ A. What is the magnitude of the magnetic field inside the solenoid, in teslas?

Inputs

length

L

0.50 m

turns

N

500

current

I

5 A

Outputs

field

B_{s}

How it's solved

Solved with MagneticFieldOfCurrents

Given

$L = 0.5$ m
$N = 500$
$I = 5$ A

Find $B_{s}$ .

Working

turns on each metre(solenoid) $n = \frac{N}{L}$
$n = \frac{500}{0.5}$
$n = 1000$ m⁻¹
field inside a long solenoid(solenoid) $B_{s} = μ_{0} \cdot n \cdot I$
$B_{s} = 1.25663706 \times 10^{−6} \cdot 1000 \cdot 5$
$B_{s} = 0.006283$ T
$B_{s} \approx 0.00628$ Tto 3 significant figures

Conclusion

Inside a long solenoid the field is even, set only by the turns on each metre and the current.

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 :inside_a_solenoid do4  kind :numerical5  describes "A solenoid of length %{length} has a radius of 1 cm and is made up of %{turns} turns. It carries a " \6            "current of %{current}. %{field}, in teslas?"7  given length: "0.5 m"8  given turns: "500"9  given current: "5 A"10  asks field: "What is the magnitude of the magnetic field inside the solenoid"11end

solution.rb

1require_relative "../questions/inside_a_solenoid"2require_relative "../science/moving_charges_and_magnetism/magnetic_field_of_currents"34solve :inside_a_solenoid, using: MagneticFieldOfCurrents do5  objects :solenoid67  take length: solenoid.length_of_the_coil8  take turns: solenoid.turns9  take current: solenoid.current1011  field = solenoid.field_inside12  answer field:, in: "T", figures: 31314  conclusion "Inside a long solenoid the field is even, set only by the turns on each metre and the current."15end

playground.rb

1require_relative "../solutions/inside_a_solenoid"23play_with :inside_a_solenoid do4  title "Inside a Solenoid"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)