Phyth::Electromagnetics::LineCharge Class Reference

Uniform line charge along a straight segment. More...

#include <LineCharge.hpp>

Inheritance diagram for Phyth::Electromagnetics::LineCharge:

Collaboration diagram for Phyth::Electromagnetics::LineCharge:

Public Member Functions
	LineCharge (const Vector3< Quantity< Meter > > &start, const Vector3< Quantity< Meter > > &end, const Quantity< CoulombPerMeter > lambda)
	Construct a uniform line 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 analytic formula.
Quantity< Coulomb >	GetTotalChargeValue () const override
	Get the total charge of the line.
Quantity< Meter >	GetMinimumDistanceTo (const Vector3< Quantity< Meter > > &point) const override
	Get the minimum distance from a point to the line segment.
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
Quantity< Volt >	AnalyticPotential (const Vector3< Quantity< Meter > > &point) const
	Analytic potential for finite line charge.
Vector3< Quantity< NewtonPerCoulomb > >	NumericalIntegrateField (const Vector3< Quantity< Meter > > &point, const int segments) const
	Numerical integration of electric field along the line.

Private Attributes
Vector3< Quantity< Meter > >	start_
Vector3< Quantity< Meter > >	end_
Vector3< Scalar >	direction_
Quantity< Meter >	length_
Quantity< CoulombPerMeter >	lambda_

Detailed Description

Uniform line charge along a straight segment.

LineCharge represents a straight segment with uniform linear charge density lambda (C/m). The electric field is computed by numerical integration (64 segments by default), while the potential uses an analytic closed-form solution.

Example: auto start = Vector3<Quantity<Meter>>(-1.0_m, 0_m, 0_m); auto end = Vector3<Quantity<Meter>>(1.0_m, 0_m, 0_m); auto lambda = 1.0e-9_C/m;

LineCharge line(start, end, lambda); auto point = Vector3<Quantity<Meter>>(0_m, 0.1_m, 0_m); auto E = line.GetElectricFieldAt(point); auto V = line.GetElectricPotentialAt(point);

Note: The field and potential diverge on the line charge itself. Querying at points on the line throws an exception.

Definition at line 28 of file LineCharge.hpp.

Constructor & Destructor Documentation

LineCharge()

Phyth::Electromagnetics::LineCharge::LineCharge ( const Vector3< Quantity< Meter > > &  start, const Vector3< Quantity< Meter > > &  end, const Quantity< CoulombPerMeter >  lambda  )

inline

Construct a uniform line charge.

Parameters

start	Starting point of the line (meters)
end	Ending point of the line (meters)
lambda	Linear charge density (C/m)

Definition at line 37 of file LineCharge.hpp.

Member Function Documentation

AnalyticPotential()

Quantity< Volt > Phyth::Electromagnetics::LineCharge::AnalyticPotential ( const Vector3< Quantity< Meter > > &  point ) const

inlineprivate

Analytic potential for finite line charge.

The formula is: V = k_E * lambda * ln((r1 + r2 + L) / (r1 + r2 - L))

where r1 = |point - start|, r2 = |point - end|, L = segment length.

Parameters

point

Position to evaluate the potential

Returns

Electric potential V (Volts)

Exceptions

std::runtime_error

If point is on the line charge

Note: The denominator (r1 + r2 - L) approaches zero when the point lies on the line segment, causing a logarithmic divergence.

Definition at line 122 of file LineCharge.hpp.

GetElectricFieldAt()

Vector3< Quantity< NewtonPerCoulomb > > Phyth::Electromagnetics::LineCharge::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 64 segments. Points on the line are skipped (their contribution is ignored).

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 55 of file LineCharge.hpp.

GetElectricPotentialAt()

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

inlineoverridevirtual

Compute the electric potential at a point using analytic formula.

The potential for a finite line charge is: V = k_E * lambda * ln((r1 + r2 + L) / (r1 + r2 - L)) where r1, r2 are distances to the endpoints and L is the segment length.

Parameters

point

Position to evaluate the potential (meters)

Returns

Electric potential V (Volts)

Exceptions

std::runtime_error

If point is on the line charge

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 72 of file LineCharge.hpp.

GetMinimumDistanceTo()

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

inlineoverridevirtual

Get the minimum distance from a point to the line segment.

Parameters

point

Position to compute distance from

Returns

Distance to the closest point on the segment (meters)

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 92 of file LineCharge.hpp.

GetTotalChargeValue()

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

inlineoverridevirtual

Get the total charge of the line.

Returns

lambda * length (Coulombs)

Implements Phyth::Electromagnetics::ChargeSource.

Definition at line 81 of file LineCharge.hpp.

NumericalIntegrateField()

Vector3< Quantity< NewtonPerCoulomb > > Phyth::Electromagnetics::LineCharge::NumericalIntegrateField ( const Vector3< Quantity< Meter > > &  point, const int  segments  ) const

inlineprivate

Numerical integration of electric field along the line.

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

Parameters

point	Evaluation point
segments	Number of line segments for integration

Returns

Electric field intensity E (N/C)

Definition at line 151 of file LineCharge.hpp.

Member Data Documentation

direction_

Vector3<Scalar> Phyth::Electromagnetics::LineCharge::direction_

private

Definition at line 101 of file LineCharge.hpp.

end_

Vector3<Quantity<Meter> > Phyth::Electromagnetics::LineCharge::end_

private

Definition at line 100 of file LineCharge.hpp.

lambda_

Quantity<CoulombPerMeter> Phyth::Electromagnetics::LineCharge::lambda_

private

Definition at line 103 of file LineCharge.hpp.

length_

Quantity<Meter> Phyth::Electromagnetics::LineCharge::length_

private

Definition at line 102 of file LineCharge.hpp.

start_

Vector3<Quantity<Meter> > Phyth::Electromagnetics::LineCharge::start_

private

Definition at line 100 of file LineCharge.hpp.

---

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

• include/Phyth/Elements/Electromagnetics/FieldSources/LineCharge.hpp