static void TestPotential(Func <LorentzVectorVariableU, LorentzVectorU> createPotential, EuclideanVector3 v) { LorentzVectorVariableU coordinates = new LorentzVectorVariableU("t", "x", "y", "z"); LorentzVectorU potential = createPotential(coordinates); LorentzVectorOperatorL del = coordinates.Del; ElectromagneticField field0 = new ElectromagneticField(potential, del); TestField(field0); ElectromagneticField field1 = field0.Transform(v); TestField(field1); TestFieldTransforms(field0.ElectricField, field0.MagneticField, field1.ElectricField, field1.MagneticField, v); CompareInvariantScalars(field0, field1); ElectromagneticField field2 = field1.Transform(-v); TestField(field2); TestFieldTransforms(field1.ElectricField, field1.MagneticField, field2.ElectricField, field2.MagneticField, -v); CompareInvariantScalars(field1, field2); Assert.AreEqual(field0.Potential, field2.Potential, "A dual transform"); Assert.AreEqual(field0.Del.ToString(), field2.Del.ToString(), "Del dual transform"); Assert.AreEqual(field0.ElectricField, field2.ElectricField, "E dual transform"); Assert.AreEqual(field0.MagneticField, field2.MagneticField, "B dual transform"); Assert.AreEqual(field0.CurrentDensity, field2.CurrentDensity, "J dual transform"); }
static void TestField(ElectromagneticField field) { TestFieldStrength(field.FieldStrengthTensor, field.ElectricField, field.MagneticField); TestDualFieldStrength(field.DualFieldStrengthTensor, field.ElectricField, field.MagneticField); TestMaxwellsEquations(field); TestBianchiIdentities(field.FieldStrengthTensor, field.Del.Invert()); TestCurrentDensity(field.CurrentDensity, field.Del); }
static void CompareInvariantScalars(ElectromagneticField field1, ElectromagneticField field2) { EuclideanVector3 E1 = field1.ElectricField; EuclideanVector3 B1 = field1.MagneticField; EuclideanVector3 E2 = field2.ElectricField; EuclideanVector3 B2 = field2.MagneticField; //Symbol comparison failure // Expected:<2(y^2+z^2)^-1>. Actual:<2(-v^2+1)^-1*(y^2+z^2)^-2*(z^2+v^2*(-z^2-y^2)+y^2)>. //Assert.AreEqual(field1.FieldStrengthTensor.InvariantScalar, field2.FieldStrengthTensor.InvariantScalar); Assert.AreEqual(field1.FieldStrengthTensor.Dot(field1.DualFieldStrengthTensor), field2.FieldStrengthTensor.Dot(field2.DualFieldStrengthTensor)); }
static void TestMaxwellsEquations(ElectromagneticField F) { Operator dt = F.Del.Scalar; EuclideanVector3Operator del = F.Del.Vector; Symbol chargeDensity = F.CurrentDensity.Scalar; EuclideanVector3 currentDensity = F.CurrentDensity.Vector; Assert.AreEqual(del.Dot(F.ElectricField), chargeDensity, "Gauss' Law:"); Assert.AreEqual(del.Dot(F.MagneticField), Symbol.Zero, "Gauss' Law for Magnetism:"); Assert.AreEqual(del.Cross(F.ElectricField) + dt * F.MagneticField, EuclideanVector3.Zero, "Faraday's Law of Induction"); Assert.AreEqual(del.Cross(F.MagneticField) - dt * F.ElectricField, currentDensity, "Ampere's Law"); }