Two Charges Apart

Q. Two charges of 7 μC and -2 μC are placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively. What is the electrostatic potential energy of the system, in joules? expects -0.70 J

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. Two charges of 7 μC $q_{f} = 7$ μC and -2 μC $q_{s} = -2$ μC are placed at (–9 cm, 0, 0) and (9 cm, 0, 0) $r_{fs} = 18$ cm respectively. What is the electrostatic potential energy of the system, in joules?

The playground

Inputs

first

q_{f}

7 μC

second

q_{s}

-2 μC

Outputs

energy

U_{fs}

The solution

Solved with PotentialEnergyOfCharges

Given

$q_{f} = 7$ μC
$q_{s} = -2$ μC
$r_{fs} = 18$ cm from “(–9 cm, 0, 0) and (9 cm, 0, 0)”

Find $U_{fs}$ .

Working

$q_{f} = 7$ μC $= 7 \times 10^{−6}$ C
$q_{s} = -2$ μC $= −2 \times 10^{−6}$ C
$r_{fs} = 18$ cm $= 0.18$ m
energy of a pair of charges(first, second) $U_{fs} = \frac{k \cdot q_{f} \cdot q_{s}}{r_{fs}}$
$U_{fs} = \frac{8.98755179 \times 10^{9} \cdot 7 \times 10^{−6} \cdot (−2 \times 10^{−6})}{0.18}$
$U_{fs} = −0.699$ J
$U_{fs} \approx −0.70$ Jto 2 significant figures

Conclusion

Opposite charges attract, so the pair has less energy together than apart: the energy is negative, and that much work separates them.

The Ruby

1require_relative "../physics"23question :two_charges_apart do4  kind :numerical5  describes "Two charges of %{first} and %{second} are placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively. " \6            "%{energy}, in joules?"7  given first: "7 μC"8  given second: "-2 μC"9  asks energy: "What is the electrostatic potential energy of the system"10end

1require_relative "../questions/two_charges_apart"2require_relative "../science/electrostatic_potential_and_capacitance/potential_energy_of_charges"34solve :two_charges_apart, using: PotentialEnergyOfCharges do5  objects :first, :second67  take first: first.charge8  take second: second.charge910  deduce_from "(–9 cm, 0, 0) and (9 cm, 0, 0)", first.distance(from: second) => "18 cm"1112  energy = first.potential_energy(by: second)13  answer energy:, in: "J", figures: 21415  conclusion "Opposite charges attract, so the pair has less energy together than apart: the energy is " \16             "negative, and that much work separates them."17end

1require_relative "../solutions/two_charges_apart"23play_with :two_charges_apart do4  title "Two Charges Apart"5end

The laws

quantity	written	units	within	from
coulomb constant	$k$	N m² C⁻²	—	PotentialEnergyOfCharges
charge	$q$	C	—	PotentialEnergyOfCharges
distance	$r$	m	—	PotentialEnergyOfCharges
potential energy	$U$	J	—	PotentialEnergyOfCharges
potential energy of ground by first	$U_{gf}$	J	—
charge of ground	$q_{g}$	C	—
charge of first	$q_{f}$	C	—
distance of ground from first	$r_{gf}$	m	—
potential energy of ground by second	$U_{gs}$	J	—
charge of second	$q_{s}$	C	—
distance of ground from second	$r_{gs}$	m	—
potential energy of first by ground	$U_{fg}$	J	—
distance of first from ground	$r_{f}$	m	—
potential energy of first by second	$U_{fs}$	J	—
distance of first from second	$r_{fs}$	m	—
potential energy of second by ground	$U_{sg}$	J	—
distance of second from ground	$r_{s}$	m	—
potential energy of second by first	$U_{sf}$	J	—
distance of second from first	$r_{sf}$	m	—

U_{oo} = \frac{k \cdot q_{o} \cdot q_{o}}{r_{oo}}

energy of a pair of charges

U_{gf} = \frac{k \cdot q_{g} \cdot q_{f}}{r_{gf}}

energy of a pair of charges(ground, first)

U_{gs} = \frac{k \cdot q_{g} \cdot q_{s}}{r_{gs}}

energy of a pair of charges(ground, second)

U_{fg} = \frac{k \cdot q_{f} \cdot q_{g}}{r_{f}}

energy of a pair of charges(first, ground)

U_{fs} = \frac{k \cdot q_{f} \cdot q_{s}}{r_{fs}}

energy of a pair of charges(first, second)

U_{sg} = \frac{k \cdot q_{s} \cdot q_{g}}{r_{s}}

energy of a pair of charges(second, ground)

U_{sf} = \frac{k \cdot q_{s} \cdot q_{f}}{r_{sf}}

energy of a pair of charges(second, first)