# Prove that e field lines go from high to low voltage sources using a given equation.

1. Sep 25, 2012

### Baygan

1. The problem statement, all variables and given/known data

In my electromagnetism lab, we had one electrode connected from the negative end of a power supply to one end of a conductive sheet, and the other electrode connected from the positive end of the supply to the other end of the conductive sheet. The potential difference of the system was 6 volts. Using a volt meter, we measured and recorded 9 sets of 5 specific voltages (.75v, 1.5v...etc), and their distances from the origin (the origin was at the bottom left corner of the sheet). We then took a blank sheet of paper and a ruler and plotted each voltage. We interpolated and drew the equipotential lines from point to point. The lab experiment then said that the electric field lines were perpendicular to the equipotential lines at each point. This makes sense because the electric field lines are emitted radially from the electrode, and thus are normal to the equipotential lines (which are arranged circumferentially at corresponding radii).

Here's my question...

How can one prove that the electric field lines go from higher to lower voltage sources and are perpendicular to the equipotential lines Using the equation below.

2. Relevant equations
The equation given is V_b-V_a = (-1)*(b-->a ∫E*ds)

3. The attempt at a solution

b is the final point of the point charge (closer to the positive electrode), and a is the initial point (farther from the electrode). Since the final point is higher in voltage than the initial point (due to the r in kq/r being smaller when the charge is closer to the positive electrode), the left side of the equation will be the positive value of the voltage at b minus the voltage at a. The right side will be E_a-E_b, due to the bounds switching because of the (-1). If the reference V_a was 0, this would mean that
V_b = Ea-Eb. This is the point where I get stuck.