Pedalling a Generator

Q. Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a 100 turn coil of area 0.10 m². The coil rotates at 0.5 Hz and it is placed in a uniform magnetic field of 0.01 T perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil, in volts? expects 0.314 V

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Q. Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a 100 $N = 100$ turn coil of area 0.10 m² $A = 0.10$ m². The coil rotates at 0.5 Hz $ν = 0.5$ Hz and it is placed in a uniform magnetic field of 0.01 T $B = 0.01$ T perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil, in volts?

The playground

Inputs

turns

N

100

area

A

0.1 m²

rate

ν

0.5 Hz

field

B

0.01 T

Outputs

peak

ε_{0}

The solution

Solved with ACGenerator

Given

$N = 100$
$A = 0.10$ m²
$ν = 0.5$ Hz
$B = 0.01$ T

Find $ε_{0}$ .

Working

peak emf of a turning coil(coil) $ε_{0} = N \cdot B \cdot A \cdot 2 \cdot π \cdot ν$
$ε_{0} = 100 \cdot 0.01 \cdot 0.1 \cdot 2 \cdot 3.14159265 \cdot 0.5$
$ε_{0} = 0.3142$ V
$ε_{0} \approx 0.314$ Vto 3 significant figures

Conclusion

The flux through the turning coil swings as a cosine, so the emf peaks at the turns times the field times the area times the angular speed.

The Ruby

1require_relative "../physics"23question :pedalling_a_generator do4  kind :numerical5  describes "Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a %{turns} turn coil of " \6            "area %{area}. The coil rotates at %{rate} and it is placed in a uniform magnetic field of %{field} " \7            "perpendicular to the axis of rotation of the coil. %{peak}, in volts?"8  given turns: "100"9  given area: "0.10 m2"10  given rate: "0.5 Hz"11  given field: "0.01 T"12  asks peak: "What is the maximum voltage generated in the coil"13end

1require_relative "../questions/pedalling_a_generator"2require_relative "../science/electromagnetic_induction/ac_generator"34solve :pedalling_a_generator, using: ACGenerator do5  objects :coil67  take turns: coil.turns8  take area: coil.area9  take rate: coil.frequency10  take field: B1112  peak = coil.peak_emf13  answer peak:, in: "V", figures: 31415  conclusion "The flux through the turning coil swings as a cosine, so the emf peaks at the turns times the " \16             "field times the area times the angular speed."17end

1require_relative "../solutions/pedalling_a_generator"23play_with :pedalling_a_generator do4  title "Pedalling a Generator"5end

The laws

quantity	written	units	within	from
pi	$π$	—	0 … ∞	ACGenerator
magnetic field	$B$	T	—	ACGenerator
turns	$N$	—	—	ACGenerator
area	$A$	m²	—	ACGenerator
frequency	$ν$	Hz	0 … ∞	ACGenerator
peak emf	$ε_{0}$	V	—	ACGenerator
peak emf of ground	$ε_{0,g}$	V	—
turns of ground	$N_{g}$	—	—
area of ground	$A_{g}$	m²	—
frequency of ground	$ν_{g}$	Hz	0 … ∞
peak emf of coil	$ε_{0}$	V	—
turns of coil	$N$	—	—
area of coil	$A$	m²	—
frequency of coil	$ν$	Hz	0 … ∞

ε_{0,c} = N_{c} \cdot B \cdot A_{c} \cdot 2 \cdot π \cdot ν_{c}

peak emf of a turning coil

ε_{0,g} = N_{g} \cdot B \cdot A_{g} \cdot 2 \cdot π \cdot ν_{g}

peak emf of a turning coil(ground)

ε_{0} = N \cdot B \cdot A \cdot 2 \cdot π \cdot ν

peak emf of a turning coil(coil)