Python 带电粒子在复合场中的动力学仿真

高中物理具有抽象性特点，由于高中生的抽象思维发展还未完全，在学习过程中难免存在一定的问题和困惑，若不能及时解决存在的这一矛盾，则对今后物理学习产生不利影响。

实践的认识的唯一来源。

但是，由于条件和技术限制，不可能每一个问题都通过做实验的方式解决。

那我们就可以结合发达的信息技术，通过软件模拟现实情况，暂时替代实验。

程序设计

运用Python编程并导入NumPy库

代码缩略图

完整代码 

import turtle as t    # 海龟画图库
import numpy as np
import time    # 时间库，用来放缩模拟速率step_xy = 50    # 坐标单位长度（像素）
E0, Arg_E0, slot_E0 = 50, 0.5 * np.pi, 4    # 电场的场强，方向，所在象限
B0, Dir_B0, slot_B0 = 0.01, -1, 1    # 磁场的场强，方向，所在象限
x, y = 0, 100    # 质点初始坐标
loc1 = np.array([x, y])    # 初始的数组形式，方便调用numpy计算class Environment:"""画环境"""def __init__(self):self.xlim = int(400)self.ylim = int(300)passdef draw_cs(self):"""画坐标系:return: 无返回值"""# 设置画笔t.speed(10)t.pensize(2)# 画x轴t.penup()t.goto(-self.xlim - 30, 0)  # 画出头t.pendown()t.goto(self.xlim, 0)# 画x轴的箭头t.penup()t.goto(self.xlim - 5, 5)t.pendown()t.goto(self.xlim, 0)t.goto(self.xlim - 5, -5)# 画x轴的点for i in range(-self.xlim, self.xlim, step_xy):# 画点t.penup()t.goto(i, 10)t.pendown()t.goto(i, 0)# 画字# t.penup()# if i == 0:  # 对0的处理#     t.goto(i - 10, - (step_xy - 50))#     t.write(i, align='center')# else:#     t.goto(i, -(step_xy - 25))#     t.write(i, align='center')# t.pendown()# 画x轴的Xt.penup()t.goto(self.xlim * 0.96, -self.xlim * 0.1)  # x的相对位置t.pendown()t.write('x', font=("Arial", 16))# 画y轴t.penup()t.goto(0, -self.ylim - 30)t.pendown()t.goto(0, self.ylim)# 画y轴的箭头t.penup()t.goto(-5, self.ylim - 5)t.pendown()t.goto(0, self.ylim)t.goto(5, self.ylim - 5)# 画y轴的点for i in range(-self.ylim, self.ylim, step_xy):# 画点t.penup()t.goto(10, i)t.pendown()t.goto(0, i)# # 画字# t.penup()# if i == 0:  # 对0的处理#     pass# else:#     t.goto(- (step_xy - 25), i - 5)#     t.write(i, align='center')# t.pendown()# 画y轴的yt.penup()t.goto(-self.ylim * 0.1, self.ylim * 0.93)  # y的相对位置t.pendown()t.write('y', font=("Arial", 16))# 恢复初始位置t.penup()t.goto(0, 0)t.pendown()t.pensize(1)passdef electric_field(self, E, Arg_E, slot_E):"""画电场:param E: 电场强度:param Arg_E: 电场方向向量辐角:param slot_E: 电场所在象限:return: 无返回值"""t.speed(speed=None)t.delay(delay=None)t.tracer(n=10, delay=None)t.pensize(1)list_start = (0, 50, -50, -50, 50)x_start = list_start[slot_E]sign = (0, 1, 1, -1, -1)signy = sign[slot_E]if Arg_E == 0.5 * np.pi:  # 90dt.pendown()for i in range(x_start, x_start // abs(x_start) * self.xlim, x_start // abs(x_start) * step_xy):t.penup()t.goto(i, signy * self.ylim)t.pendown()t.goto(i, 0)# 画箭头t.penup()t.goto(i - 5, signy * self.ylim - 5)t.pendown()t.goto(i, signy * self.ylim)t.goto(i + 5, signy * self.ylim - 5)t.penup()elif Arg_E == np.pi:t.pendown()for i in range(x_start, x_start // abs(x_start) * self.ylim, x_start // abs(x_start) * step_xy):t.penup()t.goto(signy * self.xlim, i)t.pendown()t.goto(0, i)# 画箭头t.penup()t.goto(signy * self.xlim + 5, i + 5)t.pendown()t.goto(signy * self.xlim, i)t.goto(signy * self.xlim + 5, i - 5)t.penup()elif Arg_E == 1.5 * np.pi:t.pendown()for i in range(x_start, x_start // abs(x_start) * self.xlim, x_start // abs(x_start) * step_xy):t.penup()t.goto(i, signy * self.ylim)t.pendown()t.goto(i, 0)# 画箭头t.penup()t.goto(i + 5, signy * self.ylim + 5)t.pendown()t.goto(i, signy * self.ylim)t.goto(i - 5, signy * self.ylim + 5)t.penup()elif Arg_E == 0:t.pendown()for i in range(x_start, x_start // abs(x_start) * self.ylim, x_start // abs(x_start) * step_xy):t.penup()t.goto(signy * self.xlim, i)t.pendown()t.goto(0, i)# 画箭头t.penup()t.goto(signy * self.xlim - 5, i - 5)t.pendown()t.goto(signy * self.xlim, i)t.goto(signy * self.xlim - 5, i + 5)t.penup()else:  # y = tan a * (x - b)print('不支持方向')passt.goto(x_start // abs(x_start) * self.xlim // 2, self.ylim * 1.1)  # y的相对位置t.pendown()t.write('E = ', font=("Arial", 16))t.penup()t.goto(x_start // abs(x_start) * self.xlim // 2 + 40, self.ylim * 1.1)t.write(str(E), font=("Arial", 16))t.goto(x_start // abs(x_start) * self.xlim // 2 + 80, self.ylim * 1.1)t.write('V/m', font=("Arial", 16))t.goto(0, 0)t.pendown()passdef magnetic_field(self, B, Dir_B, slot_B):"""画磁场:param B: 磁感应强度:param Dir_B: 磁场方向，1为向外，-1为向内:param slot_B: 磁场所在象限:return: 无返回值"""t.penup()x_start = [0, 0.5 * step_xy, -self.xlim + 0.5 * step_xy, -self.xlim + 0.5 * step_xy, 0.5 * step_xy]y_start = [0, 0.5 * step_xy, 0.5 * step_xy, -self.ylim + 0.5 * step_xy, -self.ylim + 0.5 * step_xy]startx = int(x_start[slot_B])starty = int(y_start[slot_B])# 画磁场if Dir_B == 1:for i in range(startx, startx + self.xlim, step_xy):for j in range(starty, starty + self.ylim, step_xy):t.goto(i, j)t.pensize(3)t.pendown()t.goto(i + 2, j)t.penup()passt.goto(0, 0)passelif Dir_B == -1:size = 3for i in range(startx, startx + self.xlim, step_xy):for j in range(starty, starty + self.ylim, step_xy):t.goto(i, j)t.pensize(size - 1)t.penup()t.goto(i + size, j + size)t.pendown()t.goto(i - size, j - size)t.penup()t.goto(i - size, j + size)t.pendown()t.goto(i + size, j - size)t.penup()t.goto(0, 0)passelse:print('错误')pass# 画文字t.goto(startx // abs(startx) * self.xlim // 2, self.ylim * 1.1 - 20)t.write('B = ', font=("Arial", 16))t.penup()t.goto(startx // abs(startx) * self.xlim // 2 + 40, self.ylim * 1.1 - 20)t.write(str(B), font=("Arial", 16))t.goto(startx // abs(startx) * self.xlim // 2 + 80, self.ylim * 1.1 - 20)t.write('T', font=("Arial", 16))t.goto(0, 0)t.penup()pass@staticmethoddef Judge(x, y):slot = Noneif y > 0:if x > 0:slot = 1elif x < 0:slot = 2else:passelif y < 0:if x > 0:slot = 4elif x < 0:slot = 3else:passelse:pass# print(slot)return slotpassclass MassPoint:"""质点"""mass = 0.001  # 质量(kg)q = 0.2  # 电荷量(C)带正负v = 100  # m/sAngle_v = -0.3 * np.pi  # radV = np.array([v * np.cos(Angle_v), v * np.sin(Angle_v)])  # 速度向量，大小(m/s)specific_charge = q / mass  # 比荷slot_now = Environment().Judge(x, y)passclass Move:@staticmethoddef ElectricFieldForce(slot):if slot == slot_E0:qE = MassPoint.q * E0F_electric = np.array([qE * np.cos(Arg_E0), qE * np.sin(Arg_E0)])else:F_electric = 0return F_electricpass@staticmethoddef LorentzForce(v1, Angle_v, slot):if slot == slot_B0:Bqv = B0 * MassPoint.q * v1  # 标量F_lorentz = np.array([Bqv * np.cos(Angle_v - Dir_B0 * np.pi / 2),Bqv * np.sin(Angle_v - Dir_B0 * np.pi / 2)])else:F_lorentz = 0return F_lorentzpass@staticmethoddef Gravity():g = 0  # 重力加速度(m/s)G = np.array([0, -MassPoint.mass * g])return Gpass@staticmethoddef Painter(T):X = np.array([0, 0])x1, y1 = x, yloc = np.array([x1, y1])slot = Environment.Judge(x1, y1)F = Move.LorentzForce(MassPoint.v, MassPoint.Angle_v, slot) + Move.ElectricFieldForce(slot) + Move.Gravity()a = F / MassPoint.massV = MassPoint.Vt.tracer(n=1, delay=None)t.goto(x1, y1)t.pendown()while True:slot = Environment.Judge(loc[0], loc[1])v = np.linalg.norm(V)print(v)if V[1] > 0:Angle_v = np.arccos(V[0] / v)elif V[1] < 0:Angle_v = -np.arccos(V[0] / v)else:if V[0] > 0:Angle_v = 0elif V[0] < 0:Angle_v = np.pielse:Angle_v = Noneslot = Environment.Judge(loc[0], loc[1])F = Move.LorentzForce(v, Angle_v, slot) + Move.ElectricFieldForce(slot) + Move.Gravity()a = F / MassPoint.massV = V + a * [T]X = X + V * [T]loc = loc + Xt.goto(loc[0], loc[1])print(X)if __name__ == '__main__':Environment().draw_cs()Environment().electric_field(E0, Arg_E0, slot_E0)Environment().magnetic_field(B0, Dir_B0, slot_B0)t.tracer(n=1, delay=None)t.penup()t.goto(x, y)Move().Painter(0.005)t.mainloop()

运行效果

问题和BUG 

轨迹总是左偏，电场线在部分象限画的有问题

本文来自互联网用户投稿，文章观点仅代表作者本人，不代表本站立场，不承担相关法律责任。如若转载，请注明出处。 如若内容造成侵权/违法违规/事实不符，请点击【内容举报】进行投诉反馈！