Electric Fields
By now, we’ve learned that objects with mass produce gravitational fields that reach out through space to pull on other objects with mass. In much the same way, objects with electric charge produce electric fields that reach out through space to pull (or push!) on other objects with charge. Electric field strength follows an inverse-square law just like gravity; we can use the following equation to calculate the electric field magnitude a distance r away from a point charge q (k is Coulomb’s constant).
Electric fields are vector quantities, which means the electric field at a certain point in space has both a magnitude and a direction. Luckily, there’s a simple rule to determine the direction of the electric field in the vicinity of a point charge: electric field vectors point radially away from positive (+) charges and radially towards negative (-) charges. At a point in space near several charged particles, we can add (as vectors) the various electric field contributions to get the net electric field at that point. Through the following equation, we can use the net electric field at a point in space to compute the electric force that an additional charged particle q (often called a “test charge”) would feel if placed at that location.
The simulation below computes the net electric field at every point in a grid around a pair of fixed charges q₁ and q₂. Play around with the magnitudes and signs of q₁ and q₂ to get a feel for how the shape of the net electric field depends on their properties. You can click and drag to adjust the positions of q₁ and q₂, and use the sliders to adjust the magnitude of their charges. You can also click anywhere on the grid to release test charges that will experience forces according to the net field at their positions (and act accordingly). Note: the simulation will not work properly on mobile devices.