Electric field for a point current in a halfspace.

This method computes the electric field for the point current in a halfspace at the set of gridded xyz locations provided. Where \(- \nabla V\) is the negative gradient of the electric potential for the point current. The electric field \(\mathbf{E}\) is:

\[\mathbf{E} = -\nabla V\]
xyz(…, 3) numpy.ndarray

Locations to evaluate at in units m.

E(…, 3) np.ndarray

Electric field of point current in units \(\frac{V}{m}\).


Here, we define a point current with current=1A in a halfspace and plot the electric field lines in the xy-plane.

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from geoana.em.static import PointCurrentHalfSpace

Define the point current.

>>> rho = 1.0
>>> current = 1.0
>>> simulation = PointCurrentHalfSpace(
>>>     current=current, rho=rho, location=None
>>> )

Now we create a set of gridded locations and compute the electric field.

>>> X, Y = np.meshgrid(np.linspace(-1, 1, 20), np.linspace(-1, 1, 20))
>>> Z = np.zeros_like(X)
>>> xyz = np.stack((X, Y, Z), axis=-1)
>>> e = simulation.electric_field(xyz)

Finally, we plot the electric field lines.

>>> e_amp = np.linalg.norm(e, axis=-1)
>>> plt.pcolor(X, Y, e_amp)
>>> cb = plt.colorbar()
>>> cb.set_label(label= 'Amplitude ($V/m$)')
>>> plt.streamplot(X, Y, e[..., 0], e[..., 1], density=0.50)
>>> plt.xlabel('x')
>>> plt.ylabel('y')
>>> plt.title('Electric Field Lines for a Point Current in a Halfspace')

(Source code, png, pdf)