A Coulomb One Electron at a Time

Q. If 1 × 10⁹ 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 on the other body? expects 198 y

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The web of concepts

given read from the words equation asked

The equations it used

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Check an answer

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?

The playground

Inputs

rate

n_{dot}

1e+09 s⁻¹

charge

q

1 C

Outputs

time

t

The solution

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 Ruby

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

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

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

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)