The Electric Field

Related to the idea of electric potential is the idea of electric field E(r). Similar to the way the electric potential is related to the potential energy, the electric field is related to the force. If a test charge (q₀) is placed at r, then the force on the test charge is

As said before the the acceleration experienced by a positively charged test particle is proportional to the steepness of the slope and in the downward direction. (Remember opposites attract, and likes repel.)

From the above statments and F=ma, we can say that the electric field is proportional the slope of the electric potential along its steepest path. Furthermore, the electric field points downhill along that path.

Elecric Field lines

To help picture the electric field, we use what are called electric field lines.

• An electric field lines is a line that always points along the direction of the electric field (i.e. downhill in the pictures we have been making).
• They begin on positive charges and end on negative charges.
• Two electric field lines cannot cross; at best they can meet on a charge.
• The number of lines in a region is proportional to the magnitude of the E-field. (You should see more in the steep regions on the pictures we have been making).
• The electric field lines are normal to (at right angles to) the equipotential surfaces. (This makes sense because electric field lines are along the direction of greatest change in the potential; while along the equipotential surfaces the potential doesn't change.)

Idenify on these plots (or a copy thereof) where the electric potential is zero and where the elctric field is zero.

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