Uniform surface charge distribution on a rectangular patch. More...

#include <SurfaceCharge.hpp>

Inheritance diagram for Phyth::Electromagnetics::SurfaceCharge:

Collaboration diagram for Phyth::Electromagnetics::SurfaceCharge:

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Public Member Functions
	SurfaceCharge (const Vector3< Quantity< Meter > > &center, const Vector3< Scalar > &u_axis, const Vector3< Scalar > &v_axis, const Quantity< Meter > width, const Quantity< Meter > height, const Quantity< CoulombPerSquareMeter > sigma)
	Construct a rectangular surface charge.

Vector3< Quantity< NewtonPerCoulomb > >	GetElectricFieldAt (const Vector3< Quantity< Meter > > &point) const override
	Compute the electric field at a point using numerical integration.

Quantity< Volt >	GetElectricPotentialAt (const Vector3< Quantity< Meter > > &point) const override
	Compute the electric potential at a point using numerical integration.

Quantity< Coulomb >	GetTotalChargeValue () const override
	Get the total charge of the surface.

Quantity< Meter >	GetMinimumDistanceTo (const Vector3< Quantity< Meter > > &point) const override
	Get the minimum distance from a point to the rectangular surface.

Quantity< CoulombPerSquareMeter >	GetSurfaceDensity () const

Public Member Functions inherited from Phyth::Electromagnetics::ChargeSource
virtual	~ChargeSource ()=default

virtual Quantity< CoulombPerCubicMeter >	GetChargeDensityAt (const Vector3< Quantity< Meter > > &point) const
	Get the charge density at a point.

Private Member Functions
Vector3< Quantity< NewtonPerCoulomb > >	NumericalIntegrateField (const Vector3< Quantity< Meter > > &point, const int nu, const int nv) const
	Numerical integration of electric field over the surface.

Quantity< Volt >	NumericalIntegratePotential (const Vector3< Quantity< Meter > > &point, const int nu, const int nv) const
	Numerical integration of electric potential over the surface.

Private Attributes
Vector3< Quantity< Meter > >	center_

Vector3< Scalar >	u_axis_

Vector3< Scalar >	v_axis_

Quantity< Meter >	width_

Quantity< Meter >	height_

Quantity< CoulombPerSquareMeter >	sigma_

Detailed Description

Uniform surface charge distribution on a rectangular patch.

SurfaceCharge represents a flat rectangular surface with uniform charge density sigma (C/m^2). The surface is defined by its center, two orthogonal axes (u and v), and dimensions (width and height).

Field and potential are computed by numerical integration over the surface using the midpoint rule. Default resolution is 32x32 segments.

Example: auto center = Vector3<Quantity<Meter>>(0_m, 0_m, 0_m); auto u_axis = Vector3<Scalar>(1, 0, 0); auto v_axis = Vector3<Scalar>(0, 1, 0); auto sigma = 1.0e-9_C/m2;

SurfaceCharge surface(center, u_axis, v_axis, 1.0_m, 1.0_m, sigma); auto point = Vector3<Quantity<Meter>>(0_m, 0_m, 0.1_m); auto E = surface.GetElectricFieldAt(point); auto V = surface.GetElectricPotentialAt(point);

Note: The field is evaluated numerically, so accuracy depends on the integration resolution.

Definition at line 34 of file SurfaceCharge.hpp.

Constructor & Destructor Documentation

◆ SurfaceCharge()

Phyth::Electromagnetics::SurfaceCharge::SurfaceCharge	(	const Vector3< Quantity< Meter > > &	center,
		const Vector3< Scalar > &	u_axis,
		const Vector3< Scalar > &	v_axis,
		const Quantity< Meter >	width,
		const Quantity< Meter >	height,
		const Quantity< CoulombPerSquareMeter >	sigma
	)

inline

Construct a rectangular surface charge.

Parameters

center	Center of the rectangle (meters)
u_axis	Direction of the width axis (must be unit vector)
v_axis	Direction of the height axis (must be unit vector)
width	Length along u_axis (meters)
height	Length along v_axis (meters)
sigma	Surface charge density (C/m^2)

u_axis and v_axis must be orthogonal. This is checked at runtime with an assert.

Definition at line 49 of file SurfaceCharge.hpp.

Member Function Documentation

◆ GetElectricFieldAt()

Vector3< Quantity< NewtonPerCoulomb > > Phyth::Electromagnetics::SurfaceCharge::GetElectricFieldAt ( const Vector3< Quantity< Meter > > & point ) const

inlineoverridevirtual

Compute the electric field at a point using numerical integration.

Parameters

point Position to evaluate the field (meters)

Returns: Electric field intensity E (N/C)

The field is integrated using the midpoint rule with 32x32 segments. Points on the surface are skipped (their contribution is ignored).

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 71 of file SurfaceCharge.hpp.

◆ GetElectricPotentialAt()

Quantity< Volt > Phyth::Electromagnetics::SurfaceCharge::GetElectricPotentialAt ( const Vector3< Quantity< Meter > > & point ) const

inlineoverridevirtual

Compute the electric potential at a point using numerical integration.

Parameters

point Position to evaluate the potential (meters)

Returns: Electric potential V (Volts)

The potential is integrated using the midpoint rule with 32x32 segments. Points on the surface are skipped (their contribution is ignored).

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 85 of file SurfaceCharge.hpp.

◆ GetMinimumDistanceTo()

Quantity< Meter > Phyth::Electromagnetics::SurfaceCharge::GetMinimumDistanceTo ( const Vector3< Quantity< Meter > > & point ) const

inlineoverridevirtual

Get the minimum distance from a point to the rectangular surface.

Parameters

point Position to compute distance from

Returns: Distance to the closest point on the surface (meters)

The closest point is found by projecting the point onto the surface plane and clamping to the rectangle bounds.

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 108 of file SurfaceCharge.hpp.

◆ GetSurfaceDensity()

Quantity< CoulombPerSquareMeter > Phyth::Electromagnetics::SurfaceCharge::GetSurfaceDensity ( ) const

inline

Returns: The surface charge density sigma (C/m^2)

Definition at line 122 of file SurfaceCharge.hpp.

◆ GetTotalChargeValue()

Quantity< Coulomb > Phyth::Electromagnetics::SurfaceCharge::GetTotalChargeValue ( ) const

inlineoverridevirtual

Get the total charge of the surface.

Returns: sigma * width * height (Coulombs)

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 94 of file SurfaceCharge.hpp.

◆ NumericalIntegrateField()

Vector3< Quantity< NewtonPerCoulomb > > Phyth::Electromagnetics::SurfaceCharge::NumericalIntegrateField	(	const Vector3< Quantity< Meter > > &	point,
		const int	nu,
		const int	nv
	)		const

inlineprivate

Numerical integration of electric field over the surface.

Uses the midpoint rule with nu * nv segments. Each segment contributes dE = k_E * dq / r^2 * hat_r.

Parameters

point	Evaluation point
nu	Number of segments along u axis
nv	Number of segments along v axis

Returns: Electric field intensity E (N/C)

Definition at line 142 of file SurfaceCharge.hpp.

◆ NumericalIntegratePotential()

Quantity< Volt > Phyth::Electromagnetics::SurfaceCharge::NumericalIntegratePotential	(	const Vector3< Quantity< Meter > > &	point,
		const int	nu,
		const int	nv
	)		const

inlineprivate

Numerical integration of electric potential over the surface.

Uses the midpoint rule with nu * nv segments. Each segment contributes dV = k_E * dq / r.

Parameters

point	Evaluation point
nu	Number of segments along u axis
nv	Number of segments along v axis

Returns: Electric potential V (Volts)

Definition at line 178 of file SurfaceCharge.hpp.

Member Data Documentation

◆ center_

Vector3<Quantity<Meter> > Phyth::Electromagnetics::SurfaceCharge::center_

private

Definition at line 125 of file SurfaceCharge.hpp.

◆ height_

Quantity<Meter> Phyth::Electromagnetics::SurfaceCharge::height_

private

Definition at line 127 of file SurfaceCharge.hpp.

◆ sigma_

Quantity<CoulombPerSquareMeter> Phyth::Electromagnetics::SurfaceCharge::sigma_

private

Definition at line 128 of file SurfaceCharge.hpp.

◆ u_axis_

Vector3<Scalar> Phyth::Electromagnetics::SurfaceCharge::u_axis_

private

Definition at line 126 of file SurfaceCharge.hpp.

◆ v_axis_

Vector3<Scalar> Phyth::Electromagnetics::SurfaceCharge::v_axis_

private

Definition at line 126 of file SurfaceCharge.hpp.

◆ width_

Quantity<Meter> Phyth::Electromagnetics::SurfaceCharge::width_

private

Definition at line 127 of file SurfaceCharge.hpp.

The documentation for this class was generated from the following file:

include/Phyth/Elements/Electromagnetics/FieldSources/SurfaceCharge.hpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SurfaceCharge()

Member Function Documentation

◆ GetElectricFieldAt()

◆ GetElectricPotentialAt()

◆ GetMinimumDistanceTo()

◆ GetSurfaceDensity()

◆ GetTotalChargeValue()

◆ NumericalIntegrateField()

◆ NumericalIntegratePotential()

Member Data Documentation

◆ center_

◆ height_

◆ sigma_

◆ u_axis_

◆ v_axis_

◆ width_