Worksheet 3: Electric Field and Potential¶

The purpose of this lab is to determine equipotential lines and electric field lines for an electric dipole and parallel plates, and compare them with theoretical predictions.

An equipotential is a region of space where every point has the same potential (the potential is constant). An equipotential line then is a line of constant potential. You can think of equipotential lines like contour lines on a map. On a map, these contour lines signify lines of constant altitude. In our case, our contour lines are equipotnetial lines and they signify a constant voltage. Equipotential lines are always perpendicular to the electric field.

Now let's talk about this mathematically. The Coulomb force is a conservative force. What this means is that work done on a point charge, by this force, moving it from point A to B in a static electric field is path independent. Work done around a closed loop is zero. We can define a potential $V$ such that its gradient is the electric field $\mathbf{E} = -\nabla V$. The voltage $V$ between two points $A$ and $B$ is defined as $V_{ab} = -\int_{a}^{b} \mathbf{E} \cdot d\mathbf{l} = V_A - V_B = \Delta V$. The voltage between these points is $\Delta V = V_A - V_B = 0$ (do not confuse this $\Delta V$ with the uncertainty, in this case the $\Delta$ actually signifies a "change in" voltage) if the points are located along a line of constant potential (the integral vanishes). Since both $\mathbf{E}$ and $d\mathbf{l}$ are not zero, but their dot product is, then everywhere along this line $\mathbf{E}$ is perpendicular to $d\mathbf{l}$.

We use a power supply to maintain a stable electric field and potential between two elctrodes in a conductive plate. This way we can take time to map the electric potential on the plate and reconstruct the field lines of the electric field between the two electrodes.

Measurement 1¶

Sources: https://en.wikipedia.org/wiki/Equipotential http://hyperphysics.phy-astr.gsu.edu/hbase/electric/equipot.html