# Optional Practical: Electric fields simulation (GeoGebra)

### Introduction

This worksheet is about how to build a GeoGebra simulation of electric field strength for two charges. By working though this exercise you will understand the vector nature of electric field. This worksheet assumes a working knowledge of how to use GeoGebra although I will try to make everything as clear as possible.

### One charge

- Add slider for Q
_{1}(Q_1 to get subscript) -1 to 1 increment 0.01.

- Add a point anywhere on the page (not on one of the axis though).
- In object properties make the point large (size 7).

Next you are going to write an equation for the E field at a distance r from this point but first you need to know how far, this is defined by adding another point, this will be your test charge.

- Add a second point somewhere close to the first.
- Add a line segment from the first to the second point.

The length of this line (a) will define the distance to the test charge but you also need to define the direction. The direction of E field is along the line joining the Q_{1} to the test charge, this can be defined by adding a vector from Q_{1} to the test charge.

- Add a vector joining the points from Q
_{1 }to the test charge. (vector u)

To display the field strength as a vector you are going to add another point at a distance will be proportional to the field strength and in the same direction as the radial vector but first you must calculate the field strength. In doing this we will assume that the charge Q_{1} is in nC.

The equation for E is

Which simplifies to E = 9Q/r^{2} for the units given

- Input E_1 = 9*Q_1/a^2 (remember a is the distance between the charges).
- Add a point close to the test charge.
- Delete the coordinates of the new point and replace with B+u

The new point C will now always be a distance a from B in the direction of vector u (try moving B around and see what happens to C) but you want the length of the vector to represent the field strength E_{1} .

- Change the coordinates of C to B+ E_1*u/a
- Add a vector from B to C.
- Hide all the unnecessary points and lines.

The distance between the charges and the magnitude of the field strength can be displayed using a text box.

### Two Charges

To calculate the field due to two charges you need to add the vectors representing the individual fields.

- Add a slider for Q
_{2} - Add a point a new point (D)
- Add a line segment from the test charge to the new charge (b)
- Add a vector from the new charge to the test charge (w).
- Input E_2=9*Q_2/b^2

The resultant field is found by adding the vectors representing the E_{1}_{ }and E_{2} we already have seen that the vector E_{1} = E_{1} u/a so the vector E_{2} = E_{2} w/b. The sum is found by simply adding these vectors.

- Input d = E_1*u/a + E_2*w/b

A vector will now appear originating from the origin. Move the charges and see how it changes. The last step is to put the vector on the test charge.

- Delete the E field vector and its point.
- Add a new point near to the test charge and change its coordinates to B + d
- Add a vector from B to the new point.
- Hide all unwanted labels and lines.
- Display values for field strength and lengths.

To make the charges blue for negative and red or positive you use the advance colour settings. You can work this out or yourself.

### Potential

You can easily add a calculation to find the potential at the position of the test charge. This is a scalar quantity so you don't need to worry about adding vectors.

- Add an equation to calculate V
- Display V on your worksheet.
- Try plotting lines of equipotential by switching on trace and moving the test charge so that the potential stays constant. (this is not easy).