Polythene Rubbed with Wool

solved ElectricCharge

Q. A polythene piece rubbed with wool is found to have a negative charge of 3 × 10⁻⁷ C $q = 3 \times 10^{−7}$ C. Estimate the number of electrons transferred?

Inputs

charge

q

3e-07 C

Outputs

electrons

n

How it's solved

Solved with ElectricCharge

Given

$q = 3 \times 10^{−7}$ C

Find $n$ .

Working

charge comes in whole electrons(polythene) $q = n \cdot e$
$3 \times 10^{−7} = n \cdot 1.60217663 \times 10^{−19}$
$n = 1.87245272 \times 10^{12}$
$n \approx 2 \times 10^{12}$ to 1 significant figure

Conclusion

Charge comes in whole electrons, so the charge divided by one electron's charge counts the electrons rubbed off the wool onto the polythene.

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 :polythene_rubbed_with_wool do4  kind :numerical5  describes "A polythene piece rubbed with wool is found to have a negative charge of %{charge}. %{electrons}?"6  given charge: "3e-7 C"7  asks electrons: "Estimate the number of electrons transferred"8end

solution.rb

1require_relative "../questions/polythene_rubbed_with_wool"2require_relative "../science/electric_charges_and_fields/electric_charge"34solve :polythene_rubbed_with_wool, using: ElectricCharge do5  objects :polythene67  take charge: polythene.charge89  electrons = polythene.number_of_charges10  answer electrons:, figures: 11112  conclusion "Charge comes in whole electrons, so the charge divided by one electron's charge counts the " \13             "electrons rubbed off the wool onto the polythene."14end

playground.rb

1require_relative "../solutions/polythene_rubbed_with_wool"23play_with :polythene_rubbed_with_wool do4  title "Polythene Rubbed with Wool"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 polythene	$q$	C	—
number of charges of polythene	$n$	—	—
charges a second of ground	$n_{dot,g}$	s⁻¹	—
charging time of ground	$t_{g}$	s	0 … 1e+12
charges a second of polythene	$n_{dot}$	s⁻¹	—
charging time of polythene	$t$	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(polythene)

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

charges gathered over a time(ground)

n = n_{dot} \cdot t

charges gathered over a time(polythene)