Flux Through a Square

Q. Consider a uniform electric field E = 3 × 10³ N/C along x. What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane, in N m²/C? expects 30 N m²/C

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Q. Consider a uniform electric field E = 3 × 10³ N/C $E = 3 \times 10^{3}$ N/C along x. What is the flux of this field through a square of 10 cm on a side $A = 100$ cm² whose plane is parallel to the yz plane, in N m²/C?

The playground

Inputs

field

E

3000 N/C

Outputs

flux

Φ

The solution

Solved with GausssLaw

Given

$E = 3 \times 10^{3}$ N/C
$A = 100$ cm² from “a square of 10 cm on a side”

Find $Φ$ .

Working

$E = 3 \times 10^{3}$ N/C $= 3000$ V/m
$A = 100$ cm² $= 0.01$ m²
flux through a face across the field(square) $Φ = E \cdot A$
$Φ = 3000 \cdot 0.01$
$Φ = 30$ N m²/C
$Φ \approx 30$ N m²/Cto 2 significant figures

Conclusion

A plane parallel to the yz plane stands square across a field along x, so the whole of its area catches the field.

The Ruby

1require_relative "../physics"23question :flux_through_a_square do4  kind :numerical5  describes "Consider a uniform electric field E = %{field} along x. %{flux} of this field through a square of " \6            "10 cm on a side whose plane is parallel to the yz plane, in N m²/C?"7  given field: "3e3 N/C"8  asks flux: "What is the flux"9end

1require_relative "../questions/flux_through_a_square"2require_relative "../science/electric_charges_and_fields/gausss_law"34solve :flux_through_a_square, using: GausssLaw do5  objects :square67  take field: E89  deduce_from "a square of 10 cm on a side", square.area => "100 cm2"1011  flux = square.electric_flux12  answer flux:, in: "N m2/C", figures: 21314  conclusion "A plane parallel to the yz plane stands square across a field along x, so the whole of its area " \15             "catches the field."16end

1require_relative "../solutions/flux_through_a_square"23play_with :flux_through_a_square do4  title "Flux Through a Square"5end

The laws

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 square	$A$	m²	—
radius of square	$r$	m	0 … ∞
electric flux of ground	$Φ_{g}$	N m²/C	—
electric flux of square	$Φ$	N m²/C	—
charge inside of ground	$q_{g}$	C	—
charge inside of square	$q$	C	—
diameter of ground	$D_{g}$	m	0 … ∞
diameter of square	$D$	m	0 … ∞
surface charge density of ground	$σ_{g}$	C/m²	—
surface charge density of square	$σ$	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 square	$E_{l}$	V/m	—
linear charge density of square	$λ$	C/m	—
field between plates of ground	$E_{p,g}$	V/m	—
field between plates of square	$E_{p}$	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(square)

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(square)

Φ_{g} = \frac{q_{g}}{ε_{0}}

gausss law(ground)

Φ = \frac{q}{ε_{0}}

gausss law(square)

A_{g} = π \cdot {D_{g}}^{2}

the surface of a sphere(ground)

A = π \cdot D^{2}

the surface of a sphere(square)

q_{g} = σ_{g} \cdot A_{g}

charge spread over a surface(ground)

q = σ \cdot A

charge spread over a surface(square)

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(square)

E_{p,g} = \frac{σ_{g}}{ε_{0}}

field between charged plates(ground)

E_{p} = \frac{σ}{ε_{0}}

field between charged plates(square)