# Electrostatics: Electric Field

The field concept is extremely difficult to understand for many beginning physics students. If you talked about the gravitational field when you learned Newton's Law of Universal Gravitation, you will be one step closer to understanding. Let's see if we can get a handle on it.

I will start with a definition of field that works for either gravity or electrostatics.

$$ \mbox{field} = \frac{\mbox{force}}{\mbox{property that feels force}} $$

In the case of electrostatics, the force is the Coulomb force, and the property that feels the force is the charge. (For the gravitational case, the force is gravity and the property is mass.)

$$ \vec E \equiv \frac{\vec F}{q} $$

For point charges, this becomes:

$$ \vec E = \frac{k\frac{Qq}{r^2}\hat r}{Q} $$

$$ \vec E = k \frac{q}{r^2}\hat r $$

Notice that there is only one charge left in this equation. Even a single charge generates an electric field which exists everywhere in space. For a single charge, the field is give by that last equation, and $\vec r$ goes from the single charge, $q$, to the point in space where you would like to calculate the electric field.

(This definition of $\vec r$ follows directly from Coulomb's Law. Recall that $r$ and $\hat r$ were defined for Coulomb's Law as the magnitude and direction of the vector that goes from $q$ to $Q$, where $Q$ was the charge we were finding the force on. That's not very convenient to use since we can now calculate a field without the second charge, $Q$. So now, $\vec r$ goes from the single charge $q$ to the empty point in space where you want to calculate the field.)

Let's do some simple examples, then talk about the idea of a field again.

Example: