.. note::
:class: sphx-glr-download-link-note
Click :ref:`here <sphx_glr_download_auto_examples_viz_helical_motion.py>` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_viz_helical_motion.py:
======================================================================
Motion of a charged particle in a combined magnetic and electric field
======================================================================
A charged particle follows a curved path in a magnetic field.
In an electric field, the particle tends to accelerate in a direction
parallel/antiparallel to the electric field depending on the nature of
charge on the particle. In a combined electric and magnetic field,
the particle moves along a helical path.
In this animation, there's a magnetic and an electric field present in +x
direction under whose influence the positively charged particle follows a
helical path.
Importing necessary modules
.. code-block:: default
from fury import window, actor, utils, ui
import numpy as np
import itertools
Let's define some variable and their description:
* `radius_particle`: radius of the point that will represent the particle
(default = 0.08)
* `initial_velocity`: initial velocity of the particle along +x
(default = 0.09)
* `acc`: acceleration of the particle along +x (due to the electric field)
(default = 0.004)
* `time`: time (default time i.e. time at beginning of the animation = 0)
* `incre_time`: value by which time is incremented for each call of
timer_callback (default = 0.09)
* `angular_frq`: angular frequency (default = 0.1)
* `phase_angle`: phase angle (default = 0.002)
.. code-block:: default
radius_particle = 0.08
initial_velocity = 0.09
acc = 0.004
time = 0
incre_time = 0.09
angular_frq = 0.1
phase_angle = 0.002
Creating a scene object and configuring the camera's position
.. code-block:: default
scene = window.Scene()
scene.zoom(1.2)
scene.set_camera(position=(10, 12.5, 19), focal_point=(3.0, 0.0, 0.0),
view_up=(0.0, 0.0, 0.0))
showm = window.ShowManager(scene,
size=(800, 600), reset_camera=True,
order_transparent=True)
showm.initialize()
Creating a blue colored arrow which shows the direction of magnetic field and
electric field.
.. code-block:: default
color_arrow = window.colors.blue # color of the arrow can be manipulated
centers = np.array([[0, 0, 0]])
directions = np.array([[1, 0, 0]])
heights = np.array([8])
arrow_actor = actor.arrow(centers, directions, color_arrow, heights,
resolution=20, tip_length=0.06, tip_radius=0.012,
shaft_radius=0.005)
scene.add(arrow_actor)
Initializing the initial coordinates of the particle
.. code-block:: default
x = initial_velocity*time + 0.5*acc*(time**2)
y = np.sin(angular_frq*time + phase_angle)
z = np.cos(angular_frq*time + phase_angle)
Initializing point actor which will represent the charged particle
.. code-block:: default
color_particle = window.colors.red # color of particle can be manipulated
pts = np.array([[x, y, z]])
charge_actor = actor.point(pts, color_particle, point_radius=radius_particle)
scene.add(charge_actor)
vertices = utils.vertices_from_actor(charge_actor)
vcolors = utils.colors_from_actor(charge_actor, 'colors')
no_vertices_per_point = len(vertices)
initial_vertices = vertices.copy() - \
np.repeat(pts, no_vertices_per_point, axis=0)
Initializing text box to display the name of the animation
.. code-block:: default
tb = ui.TextBlock2D(bold=True, position=(100, 90))
m1 = "Motion of a charged particle in a "
m2 = "combined electric and magnetic field"
tb.message = m1 + m2
scene.add(tb)
Initializing counter
.. code-block:: default
counter = itertools.count()
end is used to decide when to end the animation
.. code-block:: default
end = 200
This will be useful for plotting path of the particle
.. code-block:: default
coor_1 = np.array([0, 0, 0])
Coordinates to be plotted are changed everytime timer_callback is called by
using the update_coordinates function. The wave is rendered here.
.. code-block:: default
def timer_callback(_obj, _event):
global pts, time, incre_time, coor_1
time += incre_time
cnt = next(counter)
x = initial_velocity*time + 0.5*acc*(time**2)
y = np.sin(10*angular_frq*time + phase_angle)
z = np.cos(10*angular_frq*time + phase_angle)
pts = np.array([[x, y, z]])
vertices[:] = initial_vertices + \
np.repeat(pts, no_vertices_per_point, axis=0)
utils.update_actor(charge_actor)
# Plotting the path followed by the particle
coor_2 = np.array([x, y, z])
coors = np.array([coor_1, coor_2])
coors = [coors]
line_actor = actor.line(coors, window.colors.cyan, linewidth=3)
scene.add(line_actor)
coor_1 = coor_2
showm.render()
# to end the animation
if cnt == end:
showm.exit()
Run every 15 milliseconds
.. code-block:: default
showm.add_timer_callback(True, 15, timer_callback)
showm.start()
window.record(showm.scene, size=(800, 600), out_path="viz_helical_motion.png")
.. image:: /auto_examples/images/sphx_glr_viz_helical_motion_001.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 3.760 seconds)
.. _sphx_glr_download_auto_examples_viz_helical_motion.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: sphx-glr-download
:download:`Download Python source code: viz_helical_motion.py <viz_helical_motion.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: viz_helical_motion.ipynb <viz_helical_motion.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_