RFE/BUG 2001.09.12.001

There are several changes and enhancements required as detailed below. In addition, Gary wants a version with only a single particle (no 2 or 12 particle options). Let's call this 'Particle in Electric Field (Reduced)'. Otherwise, this applet is like the others.

url: Force/Electromagnetic/Simulate/Electric

Details:

• The data table at top right should have the colon immediately after the variable symbol, not just before the value. At present, there are two colons in the line for the time t. Delete the second one. Add a space before m/s^2 after the acceleration value.
• Change the color of the velocity vector from green to magenta. Change the color of the velocity components from black to the new official color.
• For Gary's one-particle applet, provide separate sliders for q and m, not a single q/m slider. The q-slider should let you set values of the charge in integer steps from -5 C to 5 C. The m-slider should let you enter mass values in integer steps from 1 to 5 kg. The value of q/m should be printed out in C/kg in the control box area, somewhere near the two sliders in a logical place.
• The charge sign toggle button should be deleted, because we can set the sign now with the q-slider.
• Try to re-arrange the various items on the control panel in a more logical and pleasing manner. E.g., the two buttons controlling the velocity and its components should be added to the collection of the other buttons on the left.
• Delete the question-mark Help button, and add a MAP logo bar with drop-down menu and Info file.

The following changes affect only the 2-particle and 12-particle modes and can be implemented later. Maybe it would be easiest to make a totally separate 1-particle applet for Gary, starting with a copy of the existing applet and stripping everything that is not needed.

• In the 2-particle mode, there should be two velocity vectors visible initially. Currently there is only one vector visible and adjustable. When one runs the simulation and clicks REPLAY, a second mustard vector becomes visible. It should be visible and adjustable right from the start.

  In this mode, de-activate the velocity-components button, and let the display-velocity button act on both velocity vectors, so that either both of them are displayed or hidden. (At present, the button does not do anything in this mode.) If both are displayed, keep them displayed during the motion. (At present, only the velocity vector of particle 1 moves along with the particle.)

• In the 12-particle mode, de-activate both the display-velocity and velocity-components buttons.
• In the 12-particle mode, REPLAY does not work properly. It does not move the particle back to the origin and, if one changes the field direction, the new motion is not oriented relative to the new direction.

2001.09.12 Hans Laue

BUG 2001.06.06.002

In the E-applet, the animation is incorrect when is something other then the default value.

The motion does not respond to settings of the |q|/m slider.

url: Force/Electromagnetic/Simulate/Electric

When the -vector is set to a vector that is rotated counter-clockwise a bit and the velocity vector is changed to be perpendicular to the new , and the charge is negative, the trajectory is not a parabola with the field direction at its axis. It crosses over the field direction. Perhaps the value of is not properly implemented in the animation.
2001.06.06 and 2001.09.12 Hans Laue

RFE 2001.06.06.002 STATUS: OPEN

In the B-applet, re-arrange the sliders so that they suggest the ratio m*v/(q*B).

Delete the unit 'C' with the q-slider. Relable the Mass slider with 'm'. Change the 'r' prinout.

url: Force/Electromagnetic/Simulate/Magnetic

Move the v-slider to the right of the m-slider. Move the B-slider to the right of the q-slider. This way the arrangement of the 4 sliders is in the order of the ratio m*v/(q*B) that is equal to the radius r that is printed out above.

Make sure that this arrangement works also for the small-scale version of the applet in the Explain It item. It may be useful to move the B and the 1X buttons underneath the other buttons.

Delete the unit 'C' in the q-slider. None of the other sliders have units.

Change the printout of 'r' to reflect the way 'r' is calculated. Thus, write

r = (m*v)/(q*B) = ...

Don't write any of the multiplication signs or parentheses. Write 9 in front of a fraction that is written with a real horizontal fraction bar and has 'mv' on top and 'qB' on the bottom.

Instead of the label 'Mass' for the m-slider use 'm', to be consistent with what is done for the other sliders and to introduce the symbols.
(2001.06.06) Hans Laue

BUG 2001.09.12 STATUS: OPEN

Changing values with the sliders does not always lead to correct values of r as printed out at top right.

Delete the question mark button for Help and add the MAP logo bar and link it to an info page.

url: Force/Electromagnetic/Simulate/Magnetic

Details:
The default values of m, v, q, B are 1, 1, 3, 2. Change m to 2, v to 3, and observe the corresponding changes for r. At this point, you should have r = 9. Now just click on the q-slider without moving it. The applet changes the value of r to 4.5. Of course, the value should stay at 9. I have not checked if the animation displays a radius equal to 4.5 or 9.

The values of r that should be displayed are given by the equation in the preceding RFE, namely, r = (m*v)/(q*B).
2001.09.12 Hans Laue

BUG 2001.06.06.004

In the B-applet, it can happen that clicking on the slider when q = 3 will produce a change in r-value, both the printed r-value and the simulated r-value.

url: Force/Electromagnetic/Simulate/Magnetic

When m=2, v=3, q=3, B=2, an r-value of 9 is displayed, which is correct. If one now clicks on the q slider, the slider tab, the r-value changes to 4.5 while the q value remains at 9. If one now changes the q-value to 1, the r-value increases by a factor of 3 to 13.5. Thus, things are consistent from this point on, if one takes 4.5 as correct. The system behaves as if the scale factor of 9 in front of the formula m*v/(q*B) has become reset. This effect does not occur for other settings of m, v, q, B.
(2001.06.06) Hans Laue

BUGS/RFES 2001.06.14.001

This is a copy of an email message dated 01-05-25 requesting a number of changes to the ExB applet. I am reproducing the email message below.

url: Force/Electromagnetic/Simulate/ExB Drift

Here are my thoughts on the ExB applet. I am assuming that things are programmed via a Galilean transformation to the drift frame. The steps should be as follows.

I will use the <...> notation to denote a vector, e.g., <v> to denote a velocity and v the magnitude of the velocity.

I will use vp to denote the numerical value of the variable v expressed in pixels and vu to denote the numerical value of v expressed in some given unit of v. ('u' stands for unit.) Similarly, Ep and Eu for the numerical values of E in pixels and in E-units, etc.

1. One gets <vin> in pixels from the green arrow. This yields vinp and the angle of <vin#62.
2. One calculates the drift velocity <u> = <E>X<B> in whatever units E and B may be given. First, one obtains Ep from the red arrow and then transforms Ep by means of a scale factor to a new Eu. Let the maximum value of this new Eu be 0.001, say. (I think the program has 0.5 at present.) And let the minimum value of Bu be 1. Then this would give a maximum value of uu = 0.001. (The reason I am choosing these funny values is that u must be much less than the speed of light for the equations to be physically accurate, and I am taking the speed of light equal to 1, in u-units. It would not matter if in the simulation we chose uu to be much bigger than 0.001, but it helps me in visualising things if I use uumax = 0.001.)
3. Before going to the next step one must now invent a scale factor that translates the pixel units of <vin> to u-units. Suppose we want uumax = 0.001 to be represented by 50 pixels. Then vu = 1 corresponds to 50,000 vp and 1 vp corresponds to 2x10^-5 vu. Thus, if <vin> is 100 pixels long, then vinp = 100 and vinu = 0.002.
4. In the following, let us work with a velocity scale factor such that a numerical value of vp = 1 corresponds to vu = 0.00002 and with an E-field scale factor such that an Ep = 120 (or some value like this) corresponds to Eu = 0.001.
5. Now calculate <v'in> = <v> - <u>, where <v'in> is the initial velocity in the drift frame. Here v and u must be in the same units, either pixel units or u-units. v'in will then be in these units as well.
6. Now calculate the orbit in the drift frame. This is done by calculating <v'(t)> rotating the vector by 90 deg, and multiplying it by a suitable scale factor C to get a display that fits on the screen. The resulting vector is denoted . It is the position vector in the drift frame. The scale factor C used here is unrelated to the other scale factors and is quite arbitrary because it simply determines the scale of the representation in position space. One cannot make a 'mistake' by choosing C incorrectly, other than that the circle in which the particle moves might be too large or too small for inspection.

To calculate <v'(t)>, one can use closed expressions of the form v'x = v'in*cos w*t and v'y = v'in*sin w*t, where v'in = const (calculated in Step 3) and w = (q/m)*B. w too needs to have a scale factor D which will determine the speed of the animation, i.e., the rate at which the particle is performing one revolution.

Did Jonathan use closed expressions like these or did he use a numerical integration? If one does a numerical integration, one must use for the acceleration the vector product (q/m) <v>X<B>, i.e., ax = (q/m)*B*v*y and ay = -(q/m)*B*v*x. Again, there needs to be a scale factor introduced into these equations that will determine the speed of the animation. (Varying the scale factor is equivalent to varying the size of the integration time step dt because the expressions for ax and ay are multiplied by dt.)

Step 4 yields <r'(t)>, the position vector of the particle in the drift frame, e.g.,

x'(t) = C*v'in*sin D*w*t.

It is assumed here that w is calculated in u-units for q/m and B and v'in is calculated in u-units as well. C is chosen so that x' and y' are in pixel units.

7. Now calculate <r(t)> = <r'(t)> + <u>*t, the position vector in the lab frame. We want <r(t)> in pixel units and must make sure that the two terms <r'(t)> and <u>*t are both in pixel units. We already have <r'(t)> in pixel units.

   The speed of a point on the <r'>-circle in pixels per time unit is C*v'inu*D*wu. We must introduce a scale factor F that translates uu to up = F*uu such that

   C*v'inu*D*wu/up = v'inu/uu.

   Thus,

   C*v'inu*D*wu/(F*uu) = (v'inu/uu) * (C*D*wu/F) = v'inu/uu

   whence

   C*D*wu/F = 1 or F = C*D*wu.

   Thus, we get <r(t)>p = <r'(t)>p + F*<u>u*t.

(2001.06.14) Hans Laue