A Coulomb One Electron at a Time

solved ElectricCharge

Q. If 1 × 10⁹ s⁻¹ $n_{dot} = 1 \times 10^{9}$ s⁻¹ electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C $q = 1$ C on the other body?

Inputs

rate

n_{dot}

1e+09 s⁻¹

charge

q

1 C

Outputs

time

t

How it's solved

Solved with ElectricCharge

Given

$n_{dot} = 1 \times 10^{9}$ s⁻¹
$q = 1$ C

Find $t$ .

Working

charge comes in whole electrons(other body) $q = n \cdot e$
$1 = n \cdot 1.60217663 \times 10^{−19}$
$n = 6.24150907 \times 10^{18}$
charges gathered over a time(other body) $n = n_{dot} \cdot t$
$6.24150907 \times 10^{18} = 1 \times 10^{9} \cdot t$
$t = 197.8$ y
$t = 6.24150907 \times 10^{9}$ s $= 197.781488$ y
$t \approx 198$ yto 3 significant figures

Conclusion

A coulomb is a vast number of electrons, so even a billion a second takes about two centuries to gather one.

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_coulomb_one_electron_at_a_time do4  kind :numerical5  describes "If %{rate} electrons move out of a body to another body every second, %{time} to get a total charge of " \6            "%{charge} on the other body?"7  given rate: "1e9 s-1"8  given charge: "1 C"9  asks time: "how much time is required"10end

solution.rb

1require_relative "../questions/a_coulomb_one_electron_at_a_time"2require_relative "../science/electric_charges_and_fields/electric_charge"34solve :a_coulomb_one_electron_at_a_time, using: ElectricCharge do5  objects :other_body67  take rate: other_body.charges_a_second8  take charge: other_body.charge910  time = other_body.charging_time11  answer time:, in: "y", figures: 31213  conclusion "A coulomb is a vast number of electrons, so even a billion a second takes about two " \14             "centuries to gather one."15end

playground.rb

1require_relative "../solutions/a_coulomb_one_electron_at_a_time"23play_with :a_coulomb_one_electron_at_a_time do4  title "A Coulomb One Electron at a Time"5end

The laws it drew on

quantity	written	units	within	from
elementary charge	$e$	C	—	ElectricCharge
charge	$q$	C	—	ElectricCharge
number of charges	$n$	—	—	ElectricCharge
charges a second	$n_{dot}$	s⁻¹	—	ElectricCharge
charging time	$t$	s	0 … 1e+12	ElectricCharge
charge of ground	$q_{g}$	C	—
number of charges of ground	$n_{g}$	—	—
charge of other body	$q$	C	—
number of charges of other body	$n$	—	—
charges a second of ground	$n_{dot,g}$	s⁻¹	—
charging time of ground	$t_{g}$	s	0 … 1e+12
charges a second of other body	$n_{dot}$	s⁻¹	—
charging time of other body	$t$	s	0 … 1e+12

q_{b} = n_{b} \cdot e

charge comes in whole electrons

n_{b} = n_{dot,b} \cdot t_{b}

charges gathered over a time

q_{g} = n_{g} \cdot e

charge comes in whole electrons(ground)

q = n \cdot e

charge comes in whole electrons(other body)

n_{g} = n_{dot,g} \cdot t_{g}

charges gathered over a time(ground)

n = n_{dot} \cdot t

charges gathered over a time(other body)