Electrostatic field painted by Simulation

1. Electrostatic field painted by Simulation School of Electronics & Applied Physics, Hefei University of Technology

2. Teaching purposes and requirements • 1. Learn the method to use the electric current field to simulate the electrostatic field. • 2. Survey and paint several contours of electrostatic field. • 3. Study to deal with the experimental data using least square method.

3. Experimental principle • Simulation • Shown in figure 1, supposing the length of the cylinder is no limited, the line density of electric charge is +e and –e, effective permittivity of the medium between cylinders is a, the potential is zero outside the cylinder and the inside of the cylinder is (1)

4. Experimental principle • Either potentialbetween two cylinders is ： • Comparing (1) and (2) expressions, we can obtain: (2) (3)

5. Experimental principle • The current field is Showed in figure 2. The voltage between the two cylinders is V0. Supposing the conductor thickness is t, the total resistance of conductor is (4)

6. Experimental principle • The radial current in the conductor is： • The resistance from r to R2 is： (5) (6)

7. Experimental principle • The potential of the r in the conductor is： • Comparing the potential formula of the electrostatic field with the one of the current field, they are same. So we can use the current field to simulate the electrostatic field. (7)

8. Contents and procedures of experiment • 1. Connect the circuit according to the circuit diagram • 2. Select V0 = 10V • 3. Measure the contours of 1V, 2V, 3V, 4V, 5V and 6V, measure at least 6 - 8 points for each contour • 4. Deal with the experiment data with the Least squares • 5. Draw the contour plot

9. Data processing Data table Equipotential lines

10. Data processing The radius of two cylinders R1 and R2 are worked out by least squares method （calculation） By least squares method： Relative uncertaintys are worked out by ：