The Charge Behind a Flux

solved GausssLaw

Q. A point charge causes an electric flux of -1.0 × 10³ N m²/C $Φ = −1.0 \times 10^{3}$ N m²/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. What is the value of the point charge, in nC?

Inputs

flux

Φ

-1000 N m²/C

Outputs

charge

q

How it's solved

Solved with GausssLaw

Given

$Φ = −1.0 \times 10^{3}$ N m²/C

Find $q$ .

Working

gausss law(sphere) $Φ = \frac{q}{ε_{0}}$
$(−1000) = \frac{q}{8.85418781 \times 10^{−12}}$
$q = −8.854$ nC
$q = −8.85418781 \times 10^{−9}$ C $= −8.85418781$ nC
$q \approx −8.85$ nCto 3 significant figures

Conclusion

The flux through the surface is the charge inside over the permittivity of free space; flux flowing inward means a negative charge.

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 :the_charge_behind_a_flux do4  kind :numerical5  describes "A point charge causes an electric flux of %{flux} to pass through a spherical Gaussian surface of " \6            "10.0 cm radius centred on the charge. %{charge}, in nC?"7  given flux: "-1.0e3 N m2/C"8  asks charge: "What is the value of the point charge"9end

solution.rb

1require_relative "../questions/the_charge_behind_a_flux"2require_relative "../science/electric_charges_and_fields/gausss_law"34solve :the_charge_behind_a_flux, using: GausssLaw do5  objects :sphere67  take flux: sphere.electric_flux89  charge = sphere.charge_inside10  answer charge:, in: "nC", figures: 31112  conclusion "The flux through the surface is the charge inside over the permittivity of free space; flux " \13             "flowing inward means a negative charge."14end

playground.rb

1require_relative "../solutions/the_charge_behind_a_flux"23play_with :the_charge_behind_a_flux do4  title "The Charge Behind a Flux"5end

The laws it drew on

quantity	written	units	within	from
pi	$π$	—	0 … ∞	GausssLaw
permittivity of free space	$ε_{0}$	F/m	—	GausssLaw
field strength	$E$	V/m	—	GausssLaw
area	$A$	m²	—	GausssLaw
radius	$r$	m	0 … ∞	GausssLaw
electric flux	$Φ$	N m²/C	—	GausssLaw
charge inside	$q$	C	—	GausssLaw
diameter	$D$	m	0 … ∞	GausssLaw
surface charge density	$σ$	C/m²	—	GausssLaw
linear charge density	$λ$	C/m	—	GausssLaw
field near a line	$E_{l}$	V/m	—	GausssLaw
field between plates	$E_{p}$	V/m	—	GausssLaw
area of ground	$A_{g}$	m²	—
radius of ground	$r_{g}$	m	0 … ∞
area of sphere	$A$	m²	—
radius of sphere	$r$	m	0 … ∞
electric flux of ground	$Φ_{g}$	N m²/C	—
electric flux of sphere	$Φ$	N m²/C	—
charge inside of ground	$q_{g}$	C	—
charge inside of sphere	$q$	C	—
diameter of ground	$D_{g}$	m	0 … ∞
diameter of sphere	$D$	m	0 … ∞
surface charge density of ground	$σ_{g}$	C/m²	—
surface charge density of sphere	$σ$	C/m²	—
field near a line of ground	$E_{l,g}$	V/m	—
linear charge density of ground	$λ_{g}$	C/m	—
field near a line of sphere	$E_{l}$	V/m	—
linear charge density of sphere	$λ$	C/m	—
field between plates of ground	$E_{p,g}$	V/m	—
field between plates of sphere	$E_{p}$	V/m	—

A_{f} = π \cdot {r_{f}}^{2}

a round face

Φ_{f} = E \cdot A_{f}

flux through a face across the field

Φ_{s} = \frac{q_{s}}{ε_{0}}

gausss law

A_{s} = π \cdot {D_{s}}^{2}

the surface of a sphere

q_{s} = σ_{s} \cdot A_{s}

charge spread over a surface

E_{l,l} = \frac{λ_{l}}{2 \cdot π \cdot ε_{0} \cdot r_{l}}

field of a long line of charge

E_{p,p} = \frac{σ_{p}}{ε_{0}}

field between charged plates

A_{g} = π \cdot {r_{g}}^{2}

a round face(ground)

A = π \cdot r^{2}

a round face(sphere)

Φ_{g} = E \cdot A_{g}

flux through a face across the field(ground)

Φ = E \cdot A

flux through a face across the field(sphere)

Φ_{g} = \frac{q_{g}}{ε_{0}}

gausss law(ground)

Φ = \frac{q}{ε_{0}}

gausss law(sphere)

A_{g} = π \cdot {D_{g}}^{2}

the surface of a sphere(ground)

A = π \cdot D^{2}

the surface of a sphere(sphere)

q_{g} = σ_{g} \cdot A_{g}

charge spread over a surface(ground)

q = σ \cdot A

charge spread over a surface(sphere)

E_{l,g} = \frac{λ_{g}}{2 \cdot π \cdot ε_{0} \cdot r_{g}}

field of a long line of charge(ground)

E_{l} = \frac{λ}{2 \cdot π \cdot ε_{0} \cdot r}

field of a long line of charge(sphere)

E_{p,g} = \frac{σ_{g}}{ε_{0}}

field between charged plates(ground)

E_{p} = \frac{σ}{ε_{0}}

field between charged plates(sphere)