def electric_field(self, xyz):
"""
Electric field from an electric dipole
.. math::
\mathbf{E} = \\frac{1}{\hat{\sigma}} \\nabla \\nabla \cdot \mathbf{A}
- i \omega \mu \mathbf{A}
"""
dxyz = self.vector_distance(xyz)
r = self.distance(xyz)
r = repeat_scalar(r)
thetar = self.theta * r
root_pi = np.sqrt(np.pi)
front = ((self.current * self.length) /
(4 * np.pi * self.sigma * r**3))
symmetric_term = (
(-(4 / root_pi * thetar**3 + 6 / root_pi * thetar) *
np.exp(-thetar**2) + 3 * erf(thetar)) *
(repeat_scalar(self.dot_orientation(dxyz)) * dxyz / r**2))
oriented_term = ((4. / root_pi * thetar**3 + 2. / root_pi * thetar) *
np.exp(-thetar**2) - erf(thetar)) * np.kron(
self.orientation, np.ones((dxyz.shape[0], 1)))
return front * (symmetric_term + oriented_term)
def magnetic_field(self, xyz):
"""
Magnetic field due to a magnetic dipole in a wholespace
"""
dxyz = self.vector_distance(xyz)
r = repeat_scalar(self.distance(xyz))
kr = self.wavenumber * r
ikr = 1j * kr
front_term = self.moment / (4. * np.pi * r**3) * np.exp(-ikr)
symmetric_term = (repeat_scalar(self.dot_orientation(dxyz)) * dxyz *
(-kr**2 + 3 * ikr + 3) / r**2)
oriented_term = ((kr**2 - ikr - 1) *
np.kron(self.orientation, np.ones(
(dxyz.shape[0], 1))))
return front_term * (symmetric_term + oriented_term)
def electric_field(self, xyz):
"""
Electric field from a magnetic dipole in a wholespace
"""
dxyz = self.vector_distance(xyz)
r = repeat_scalar(self.distance(xyz))
kr = self.wavenumber * r
ikr = 1j * kr
front_term = ((1j * self.omega * self.mu * self.moment) /
(4. * np.pi * r**2) * (ikr + 1) * np.exp(-ikr))
return front_term * self.cross_orientation(dxyz) / r
def magnetic_field_time_deriv(self, xyz):
"""
Time derivative of the magnetic field,
:math:`\\frac{\partial \mathbf{h}}{\partial t}`
"""
dxyz = self.vector_distance(xyz)
r = self.distance(dxyz)
r = repeat_scalar(r)
front = (self.current * self.length * self.theta**3 * r /
(2 * np.sqrt(np.pi)**3 * self.time))
return -front * self.cross_orientation(xyz) / r
def magnetic_field(self, xyz):
"""
Magnetic field from an electric dipole
"""
dxyz = self.vector_distance(xyz)
r = self.distance(dxyz)
r = repeat_scalar(r)
thetar = self.theta * r
front = (
self.current * self.length / (4 * np.pi * r**2) *
(2 / np.sqrt(np.pi) * thetar * np.exp(-thetar**2) + erf(thetar)))
return -front * self.cross_orientation(xyz) / r
def electric_field(self, xyz):
"""
Electric field from an electric dipole
.. math::
\\mathbf{E} = \\frac{1}{\\hat{\\sigma}} \\nabla \\nabla \\cdot
\\mathbf{A}
- i \\omega \\mu \\mathbf{A}
"""
dxyz = self.vector_distance(xyz)
r = repeat_scalar(self.distance(xyz))
kr = self.wavenumber * r
ikr = 1j * kr
front_term = ((self.current * self.length) /
(4 * np.pi * self.sigma * r**3) * np.exp(-ikr))
symmetric_term = (repeat_scalar(self.dot_orientation(dxyz)) * dxyz *
(-kr**2 + 3 * ikr + 3) / r**2)
oriented_term = ((kr**2 - ikr - 1) *
np.kron(self.orientation, np.ones(
(dxyz.shape[0], 1))))
return front_term * (symmetric_term + oriented_term)
def magnetic_field(self, xyz):
"""
Magnetic field from an electric dipole
.. math::
\\mathbf{H} = \\nabla \\times \\mathbf{A}
"""
dxyz = self.vector_distance(xyz)
r = repeat_scalar(self.distance(xyz))
kr = self.wavenumber * r
ikr = 1j * kr
front_term = (self.current * self.length / (4 * np.pi * r**2) *
(ikr + 1) * np.exp(-ikr))
return -front_term * self.cross_orientation(dxyz) / r