BELIEVE   ME   NOT!    - -     A   SKEPTICs   GUIDE  

The Electric Field

The ELECTRIC FIELD $\Vec{E}$ at any point in space is defined to be the force per unit test charge due to all the other charges in the universe. That is, there is probably no ``test charge'' q there to experience any force, but if there were it would experience a force

$$\Vec{F}_E \; = \; q \; \Vec{E}$$ (17.5)

Note that since the force is a vector, $\Vec{E}$ is a vector field.

Since by definition $\Vec{E}$ is there even if there isn't any test charge present, it follows that there is an electric field at every point in space, all the time! [It might be pretty close to zero, but it's still there!]^17.4

Is the ELECTRIC FIELD real? No. Yes. You decide.^17.5 This paradigm makes everything so much easier that most Physicists can't imagine thinking about ${\cal E}$&${\cal M}$ any other way. Does this blind us to other possibilities? Undoubtedly.

A single isolated electric ``source'' charge Q [I am labelling it differently from my ``test'' charge q just to avoid confusion. Probably it won't work.] generates a spherically symmetric electric field

$$\Vec{E} \; = \; k_E \; {Q \over r^2} \; \hat{r}$$ (17.6)

at any point in space specified by the vector distance $\Vec{r}$ from Q to that point. That is, the field $\Vec{E}$ is radial [in the direction of the radius vector] and has the same magnitude E at all points on an imaginary spherical surface a distance r from Q.

It might be helpful to picture the acceleration of gravity as a similar vector field:

$$\Vec{g} \; = \; -G \; {M_E \over r^2} \; \hat{r}$$ (17.7)

-- i.e. $\Vec{g}$ always points back toward the centre of the Earth (mass M_E) and drops off as the inverse square of the distance r from the centre of the Earth.