Gradient is the generalization of the slope to three dimensions. The gradient represents the change in a quatity divided by the distance overwhich that change occurs; hence, it is the vector slope. In what possible direction can the slope point? To see why slope has a direction, you will go back to the program EM Field and use a differential approximation,
that is, we will approximate the gradient as the change in potential over change in distance.
Set up two equal signed 3D point charges. From the "Fields" menu choose "Equipotential" and click to produce a few relatively closely spaced equipotentials.
1) In the "Fields" menu switch it to "Potentials". Starting at one of the middle equipotential linds, find a line along which the gradient is zero. In what direction did you travel relative to the equipotential?
2) Find a line along which V increases maximally. In what direction did you travel relative to the equipotential line? Did you travel toward the charge or away from the charge? Leave EM field set up as it is--don't change it.
In what direction do you think the gradient points? Record your reasons in your journal.
The electric field is in the opposite direction to the gradient.
3) With the same setup as before in EM Field, choose "Field Vectors" from the "Fields" menu. Click at the point you started your collection of points for the largest gradient. In what direction does the field point relative to the gradient?
From your excursions you should see that the electric field flows down the potential hill, opposite to the gradient.
Although it is hard to see in the 3D movie, the electric field vectors move outward, away from high potential. The electric fieldlines are tangent to the vectors and a 2D plot shows the structure very well.
Go to Dipole.