Two Small Spheres Thirty Centimetres Apart

Q. Two small charged spheres having charges of 2 × 10⁻⁷ C and 3 × 10⁻⁷ C are placed 30 cm apart in air. What is the force between them, in newtons? expects 0.0060 N

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Q. Two small charged spheres having charges of 2 × 10⁻⁷ C $q_{f} = 2 \times 10^{−7}$ C and 3 × 10⁻⁷ C $q_{s} = 3 \times 10^{−7}$ C are placed 30 cm $r_{fs} = 30$ cm apart in air. What is the force between them, in newtons?

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Inputs

first

q_{f}

2e-07 C

second

q_{s}

3e-07 C

apart

r_{fs}

30 cm

Outputs

force

F_{e,fs}

The solution

Solved with CoulombsLaw

Given

$q_{f} = 2 \times 10^{−7}$ C
$q_{s} = 3 \times 10^{−7}$ C
$r_{fs} = 30$ cm

Find $F_{e,fs}$ .

Working

$r_{fs} = 30$ cm $= 0.3$ m
coulombs law(first, second) $F_{e,fs} = \frac{k \cdot q_{f} \cdot q_{s}}{{r_{fs}}^{2}}$
$F_{e,fs} = \frac{8.98755179 \times 10^{9} \cdot 2 \times 10^{−7} \cdot 3 \times 10^{−7}}{{0.3}^{2}}$
$F_{e,fs} = 0.005992$ N
$F_{e,fs} \approx 0.0060$ Nto 2 significant figures

Conclusion

Like charges push each other apart with a force that grows with each charge and falls off as the square of the distance between them.

The Ruby

1require_relative "../physics"23question :two_small_spheres_thirty_centimetres_apart do4  kind :numerical5  describes "Two small charged spheres having charges of %{first} and %{second} are placed %{apart} apart in air. " \6            "%{force}, in newtons?"7  given first: "2e-7 C"8  given second: "3e-7 C"9  given apart: "30 cm"10  asks force: "What is the force between them"11end

1require_relative "../questions/two_small_spheres_thirty_centimetres_apart"2require_relative "../science/electric_charges_and_fields/coulombs_law"34solve :two_small_spheres_thirty_centimetres_apart, using: CoulombsLaw do5  objects :first, :second67  take first: first.charge8  take second: second.charge9  take apart: first.separation(from: second)1011  force = first.electric_force(by: second)12  answer force:, in: "N", figures: 21314  conclusion "Like charges push each other apart with a force that grows with each charge and falls off as the " \15             "square of the distance between them."16end

1require_relative "../solutions/two_small_spheres_thirty_centimetres_apart"23play_with :two_small_spheres_thirty_centimetres_apart do4  title "Two Small Spheres Thirty Centimetres Apart"5end

The laws

quantity	written	units	within	from
charge	$q$	C	—	CoulombsLaw
coulomb constant	$k$	N m² C⁻²	—	CoulombsLaw
separation	$r$	m	0 … ∞	CoulombsLaw
electric force	$F_{e}$	N	—	CoulombsLaw
electric force on ground by first	$F_{e,gf}$	N	—
charge of ground	$q_{g}$	C	—
charge of first	$q_{f}$	C	—
separation of ground from first	$r_{gf}$	m	0 … ∞
electric force on ground by second	$F_{e,gs}$	N	—
charge of second	$q_{s}$	C	—
separation of ground from second	$r_{gs}$	m	0 … ∞
electric force on first by ground	$F_{e,fg}$	N	—
separation of first from ground	$r_{f}$	m	0 … ∞
electric force on first by second	$F_{e,fs}$	N	—
separation of first from second	$r_{fs}$	m	0 … ∞
electric force on second by ground	$F_{e,sg}$	N	—
separation of second from ground	$r_{s}$	m	0 … ∞
electric force on second by first	$F_{e,sf}$	N	—
separation of second from first	$r_{sf}$	m	0 … ∞

F_{e,oo} = \frac{k \cdot q_{o} \cdot q_{o}}{{r_{oo}}^{2}}

coulombs law

F_{e,gf} = \frac{k \cdot q_{g} \cdot q_{f}}{{r_{gf}}^{2}}

coulombs law(ground, first)

F_{e,gs} = \frac{k \cdot q_{g} \cdot q_{s}}{{r_{gs}}^{2}}

coulombs law(ground, second)

F_{e,fg} = \frac{k \cdot q_{f} \cdot q_{g}}{{r_{f}}^{2}}

coulombs law(first, ground)

F_{e,fs} = \frac{k \cdot q_{f} \cdot q_{s}}{{r_{fs}}^{2}}

coulombs law(first, second)

F_{e,sg} = \frac{k \cdot q_{s} \cdot q_{g}}{{r_{s}}^{2}}

coulombs law(second, ground)

F_{e,sf} = \frac{k \cdot q_{s} \cdot q_{f}}{{r_{sf}}^{2}}

coulombs law(second, first)