from abc import ABC, abstractmethod
import numpy as np
[docs]
def space_dirderivative(f, xyz, t, direction, h=1e-8):
direction = np.array(direction)
norm = np.linalg.norm(direction)
if norm == 0:
return np.zeros_like(f(*xyz, t))
direction = direction / norm # Normalize the direction vector
x, y, z = xyz
dx, dy, dz = direction * h
return (f(x + dx, y + dy, z + dz, t) - f(x - dx, y - dy, z - dz, t)) / (2 * h)
[docs]
class EBField(ABC):
@abstractmethod
def __init__(self, *args, **kwargs):
"""示范性构造函数，不允许直接实例化"""
pass
@abstractmethod
[docs]
def E_at(self, x, y, z, t):
"""Calculate the electric field at a given point and time."""
pass
@abstractmethod
[docs]
def B_at(self, x, y, z, t):
"""Calculate the magnetic field at a given point and time."""
pass
[docs]
def B_abs_at(self, x, y, z, t):
return np.linalg.norm(self.B_at(x, y, z, t))
[docs]
def E_and_B_at(self, x, y, z, t):
return self.E_at(x, y, z, t), self.B_at(x, y, z, t)
[docs]
def hatb_at(self, x, y, z, t):
return self.B_at(x, y, z, t) / np.linalg.norm(self.B_at(x, y, z, t))
[docs]
def vE_at(self, x, y, z, t):
return np.cross(self.E_at(x, y, z, t), self.hatb_at(x, y, z, t)) / self.B_abs_at(x, y, z, t)
[docs]
def gradB_abs_at(self, x, y, z, t):
xyz = np.array([x, y, z])
return np.array([
space_dirderivative(self.B_abs_at, xyz, t, [1,0,0]),
space_dirderivative(self.B_abs_at, xyz, t, [0,1,0]),
space_dirderivative(self.B_abs_at, xyz, t, [0,0,1]),
])
[docs]
def kappa_at(self, x, y, z, t):
return space_dirderivative(self.hatb_at, np.array([x, y, z]), t, self.hatb_at(x, y, z, t))