Electric Field and Potential Simulation

About this experiment

Every charge surrounds itself with an electric field, a push or pull that any other charge feels, and a potential, the energy per coulomb a charge would have at each point. Place positive and negative charges, watch the field lines run from plus to minus and the equipotential lines cross them at right angles, and move a probe to measure the field strength and the potential anywhere. The patterns for a dipole, two like charges and a parallel plate capacitor appear in every physics course from GCSE and AP to the IB and university.

Learning goals

Calculate the field and potential of a point charge and add the contributions of several charges
Draw field lines for common arrangements and explain what their spacing shows
Explain why equipotential lines always cross field lines at right angles
Relate field strength to the spacing of equipotentials, E = −dV/dx
Describe the nearly uniform field between parallel plates

How to use it

1Choose One charge. Move the probe to 10 cm and then to 20 cm from the charge. By what factor do E and V change?
2Choose Dipole. Find the line where V = 0. Is the field also zero there?
3Choose Like charges and look for the point where the field is zero. What happens to the field lines there?
4Choose +3 and −1. Why do some field lines from the +3 charge never reach the −1 charge?
5Choose Parallel plates. Move the probe between the plates. How does E change? Compare the spacing of equipotentials inside and outside.
6Switch on the field arrows and compare their direction with the field lines and the equipotentials.

The model

E = \frac{k q}{r ^{2}}, V = \frac{k q}{r}

Field strength and potential of a point charge

E = i \sum \frac{k q _{i}}{r _{i}^{2}} r^_{i}, V = i \sum \frac{k q _{i}}{r _{i}}

Superposition: add fields as vectors, potentials as numbers

E_{x} = - \frac{\partial V}{\partial x}

The field points downhill in potential, strongest where equipotentials are closest

E = \frac{V}{d}

Uniform field between parallel plates with potential difference V and separation d

Assumptions

Charges are points fixed in a vacuum, drawn as small discs. The field is shown in the plane of the screen only.
Field lines start on positive charges, six per nanocoulomb, and end on negative charges or leave the screen. If the negative charge is larger, they are drawn from the negative charges instead.
The parallel plates are modelled as two rows of seven point charges, so the field between them is close to, but not exactly, uniform.
Potential is measured relative to zero at infinite distance.

Try this in class

Q1A +2 nC charge is 0.10 m away. What are E and V there?
Q2Two charges of +4 nC and +1 nC are 0.30 m apart. Where on the line between them is the field zero?
Q3Why can two field lines never cross?
Q4How much work is done moving a charge along an equipotential line?
Q5Plates 2.0 cm apart are connected to 100 V. What is the field between them, and what force does a 1 nC charge feel?

Frequently asked questions

Do field lines really exist?

No, they are a drawing tool invented by Michael Faraday. The direction of a line shows the force on a positive charge and the density of lines shows the field strength. The field itself exists at every point, between the lines too.

Why is the potential negative near a negative charge?

Potential is the work per coulomb needed to bring a positive test charge in from far away. Near a negative charge the test charge is pulled in, so the work done by you is negative and so is the potential.

Can the field be zero where the potential is not, or the other way round?

Yes. Midway between two equal like charges the field is zero but the potential is not. Midway between a dipole the potential is zero but the field is strong. The field depends on how fast V changes, not on its value.