Click on a number to view the explanation of the corresponding item.

Basic Control Buttons

There are four basic control buttons. They are, from left to right:

Rewind. Resets the simulation to the initial position with the previously set initial values. If you have the particle path displayed, Rewind will allow you to compare paths traversed under different conditions, e.g., different initial velocities. After clicking Rewind, click Play to restart the motion.

Play/Pause. Starts the motion.

After Play has been clicked, the button will change into the Pause button.

Clicking Pause will freeze the motion. To resume the motion, click Play once more.

Step. Lets you step through the motion in equal time steps.

Reset. Resets the applet to its default setting.

Adjustments in the initial conditions can only be made after first clicking REPLAY or RESET.



Set Initial Position

To set the particle's initial position, click on the particle and drag. To make it easier to achieve a certain set of initial (x,y) values, hold down the SHIFT key while dragging the particle. This will allow dragging in either the horizontal or vertical directions only, thus making it easier to set one of the two coordinates at a time. The particle's position coordinates can be read in the Data box.

When the particle is at the position you want, click the Initial button . This will accomplish four things.

• It will make the applet remember this position. If you click REWIND after PLAYing the motion, the particle will be returned to this position.
• It will make the applet remember the particle's initial velocity. If you click REWIND after PLAYing the motion, the particle will be returned to its initial position with its initial velocity.
• It will cause the particle's displacement vector to be taken from this initial point.
• It will set the potential and kinetic energies in the energy bar that is labeled "initial" to the values at this initial position. The energy values displayed by the "initial" bar will not change during the subsequent motion. More about the energy bars in Point 11 below.



Particles Path

Displays or hides the particle's path in cyan.

The path is not erased when you click the Rewind button.



Grid

When the Grid button is selected, a rectangular set of coordinate grid lines is displayed.

The grid makes it easier to set the particle's initial position and to observe the particle's path.

To set the particle's initial position, click on the particle and drag. To make it easier to achieve a certain set of initial (x,y) values, hold down the SHIFT key while dragging the particle. This will allow dragging in either the horizontal or vertical directions only, thus making it easier to set one of the two coordinates at a time. See Point 2 above on how to lock the initial position.



Vectors

This toggle button displays or hides the Vector Panel shown below on which you can select the vectors that you want to have displayed. In the example shown below, three vectors are selected: Electric Field, Acceleration, and Velocity. Displacement is not selected.

The electric field vector, if selected on the panel, will be displayed at any field point set by you. See Point 7 below on how to set a field point.

Electric field vectors will be shown in green. The acceleration, velocity, and displacement vectors will be shown in orange, magenta, and cyan, respectively.





Data



Displays or hides the draggable Data box, shown above, as well as the draggable Energy box. The latter, which shows energy bars, can be seen in the picture at the beginning of this Help file. In that picture, the Data box has been closed by clicking the "X" in the upper right-hand of the Data box. Information about the Energy box is provided in Point 11 below.

The Data box displays the following information:

• k: the universal constant in Coulomb's Law
• t: time elapsed since the beginning of the motion
• (x,y): coordinates of the particle at time t relative to a coordinate grid that can be displayed by selecting the Grid button; the x-axis points to the right, the y-axis upward
• r: distance of the particle from the center of the source charge
• (d_x,d_y): displacement of the particle at time t, measured either from the particle's default position or from the position at which the Initial button was clicked; see Point 2 above for details about this button
• (a_x,a_y): acceleration of the particle at time t
• KE: kinetic energy of the particle at time t
• PE: potential energy of the particle in the electric field at time t where PE is defined so that PE = 0 when the particle is at (x,y) = (0,0)
• E = PE + KE: energy of the particle in the electric field with PE defined as above
• V: electric potential at the location of the particle



Coordinates

When the Coordinates button is selected, clicking at some location in the applet window will mark that location with a "+" and display the x,y coordinates of the location. This way you can measure the coordinates of a field point. The electric potential in volt (V) at that point will be displayed also.

The field point can be dragged to a new location as long as the mouse button is depressed. If the SHIFT key is held down while dragging, the field point will move only in the horizontal or vertical directions. As many field points as are needed can be marked in this manner.

One can return the mouse pointer to an existing location marker at a later time and drag the marker then.

Double-clicking on a field point marker will remove it, but only if the Coordinates button is selected at the time. One can remove a marker at any time, even if the Coordinates button had been deselected after placing the marker, as long as this button is selected when one double-clicks on the marker.



Field Line
Equipotential Line

When a field point marker has been set at some point as explained in the preceding Point 7, the electric field line (in green) and equipotential line (in mustard color) through that point can be displayed by clicking the Field-Line or Equipotential-Line button, respectively. The equipotential "lines" are actually circles in this case, the source charge being at the center of the circles.

When a line is displayed, its button becomes inactive. It becomes active again when another field point marker is set.

Dragging the field point marker will cause the field line and equipotential line through that point to be dragged along.



Velocity Vector

Two data fields are available to specify the initial velocity vector. Enter values in the two fields and press ENTER on the keyboard to set the initial velocity. The magenta velocity vector will be adjusted accordingly. Alternatively, you can drag the tip of the velocity vector. The values in the two velocity data fields will be adjusted accordingly.

During the motion, the values in the velocity data fields and the magenta arrow, if displayed, will represent the instantaneous velocity.

Four different modes are available for specifying the velocity vector numerically. Choose between them by clicking the button to the left of the velocity data entry fields. The button will let you cycle through the four possibilities:

1. Polar (positive)

   The vector is specified by its polar coordinates: magnitude and direction angle. The direction angle is taken between the vector and the 'East' direction (positive x direction). All angles are positive between 0 and 360⁰, increasing in the counter-clockwise sense starting with the East direction.

2. Polar (pos & neg)

   The mode is like the Polar (positive) mode, except that the angles are taken to be in the range from -180⁰ to 180⁰. The angle is negative if a vector points to a point below the horizontal axis, and it is positive otherwise.

3. Navigational

   The mode is like the Polar (positive) mode, except that angles are taken relative to one of the four compass directions, either in the clockwise or counter-clockwise sense. This allows for eight different ways of specifying the angle, from east of north (E of N), to north of east (N of E), to west of north (W of N). The choice can be made from a drop-down menu that becomes available in the Navigational mode. All angles range from 0 to 360⁰.

4. Cartesian (v_x,v_y)

   The vector is specified by its x and y components relative to the horizontal x-axis and the vertical y-axis.



Sliders




There are three sliders, for adjusting the charge of the source and the charge and mass of the test particle. The source and test charges can be varied from -3 mC to 3 mC in steps of 1 mC. The test mass can be varied from 1.0 kg to 3.0 kg in steps of 0.1 kg.

Clicking on a slider to the left or right of the slider tab allows fine adjustment of the slider setting.

Clicking on the Input Dialog button of a slider will open a dialog for entering an exact value for the slider setting. The dialog for the Charge-slider is illustrated below. The range in which values can be entered, from -3 C to 3 C in this case, is indicated above the data entry field.



The source charge is shown in red when positive and in blue when negative. An uncharged source is shown in grey.

The test particle is represented by a small colored disk: colored red when the particle's charge is positive, blue when negative, and grey when zero.



Energy Bars



When the Data button is selected, two draggable boxes are displayed: the Data box (see Point 6 above) and the Energy box, shown in the preceding image.

The Energy box contains three columns, which display from left to right:

• the electric potential V at the current particle position,
• the current kinetic energy KE and current electric potential energy PE of the particle,
• the initial kinetic and electric potential energies of the particle.

The "initial" moment to which the kinetic and potential energies correspond is the moment when the Initial button is clicked. If this button is not clicked, then the default energies upon resetting the applet are taken as the initial energies.

The horizontal black line across the middle of the energy bars indicates the level of zero potential energy and zero electric potential. The potential energy and the electric potential are taken to be zero when the particle or the field point, respectively, are at an infinite distance from the source.



Energy Zoom Slider

The Energy box contains a vertical slider in its upper left region. See the image in the preceding Point 12. The short cross bar can be dragged up or down to increase or decrease, respectively, the height of the energy and potential bars measured from the zero level.

The scale factor that determines the size of the bars is applied to the potential energy and the electric potential relative to their zero level, i.e., such that the level indicated by the line crossing all three bars remains in the same position.