A Coil of a Hundred Turns

Q. Consider a tightly wound 100-turn coil of radius 10 cm, carrying a current of 1 A. What is the magnitude of the magnetic field at the centre of the coil, in teslas? expects 6.28 × 10⁻⁴ T

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The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. Consider a tightly wound 100 $N = 100$ -turn coil of radius 10 cm $R = 10$ cm, carrying a current of 1 A $I = 1$ A. What is the magnitude of the magnetic field at the centre of the coil, in teslas?

The playground

Inputs

turns

N

100

radius

R

10 cm

current

I

1 A

Outputs

field

B_{c}

The solution

Solved with MagneticFieldOfCurrents

Given

$N = 100$
$R = 10$ cm
$I = 1$ A

Find $B_{c}$ .

Working

$R = 10$ cm $= 0.1$ m
field at the centre of a coil(coil) $B_{c} = \frac{μ_{0} \cdot N \cdot I}{2 \cdot R}$
$B_{c} = \frac{1.25663706 \times 10^{−6} \cdot 100 \cdot 1}{2 \cdot 0.1}$
$B_{c} = 6.283 \times 10^{−4}$ T
$B_{c} \approx 6.28 \times 10^{−4}$ Tto 3 significant figures

Conclusion

Every turn adds its own field at the centre, each the current over twice the radius times μ₀.

The Ruby

1require_relative "../physics"23question :a_coil_of_a_hundred_turns do4  kind :numerical5  describes "Consider a tightly wound %{turns}-turn coil of radius %{radius}, carrying a current of %{current}. " \6            "%{field}, in teslas?"7  given turns: "100"8  given radius: "10 cm"9  given current: "1 A"10  asks field: "What is the magnitude of the magnetic field at the centre of the coil"11end

1require_relative "../questions/a_coil_of_a_hundred_turns"2require_relative "../science/moving_charges_and_magnetism/magnetic_field_of_currents"34solve :a_coil_of_a_hundred_turns, using: MagneticFieldOfCurrents do5  objects :coil67  take turns: coil.turns8  take radius: coil.radius9  take current: coil.current1011  field = coil.field_at_the_centre12  answer field:, in: "T", figures: 31314  conclusion "Every turn adds its own field at the centre, each the current over twice the radius times μ₀."15end

1require_relative "../solutions/a_coil_of_a_hundred_turns"23play_with :a_coil_of_a_hundred_turns do4  title "A Coil of a Hundred Turns"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 coil	$B_{c}$	T	—
turns of coil	$N$	—	—
current of coil	$I$	A	—
radius of coil	$R$	m	—
turns per length of ground	$n_{g}$	m⁻¹	—
length of the coil of ground	$L_{g}$	m	—
turns per length of coil	$n$	m⁻¹	—
length of the coil of coil	$L$	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 coil	$B_{w}$	T	—
distance from the wire of coil	$d$	m	—
field inside of ground	$B_{s,g}$	T	—
field inside of coil	$B_{s}$	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(coil)

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

turns on each metre(ground)

n = \frac{N}{L}

turns on each metre(coil)

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(coil)

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(coil)