A correspondent writes in:
I've been telling my class that the electric field cannot be negative. 1. Its direction is set and then 2. the value is set. And since the value corresponds to the predetermined direction, it is always positive.
One of my international students from China used the vector argument. Since electric field is a vector quantity, can't we 1. choose our direction first - independent of the field and then 2. determine the direction of the electric field and how it meshes with our predetermined direction? Was I terribly wrong to say that E-field cannot be negative?
My response: I say an electric field can never "be negative." Electric field is a vector -- it has magnitude and direction.
Sometimes in a 1-dimensional problem, by convention physicists choose one direction to be positive, one negative. For example, if south is the negative direction, then a car slowing down moving north might have a "positive" velocity and "negative" acceleration. And the kinematics equations require algebraic use of the negative signs. Nevertheless, the magnitude of the acceleration vector would still be 4 m/s/s*, and the direction would be south; the magnitude of the acceleration can never be - 4 m/s/s.
* not even positive 4 m/s/s, just plain ol' 4 m/s/s
It's legitimate, though crude, to apply the same reasoning to the electric field. Define up as positive. Then a 200 N/C electric field that points down could be called "-200 N/C."
But there is NO REASON EVER TO DO THIS IN INTRODUCTORY PHYSICS. EVER.
(You can see some of my reasoning in this post: Never trust a student with a negative sign.)
Students get into trouble if they try to use F=qE, and plug in negative signs for q and E to get negative forces. Negative forces? What are they? Forces also have magnitude and direction. You can't have a -300 N force, just a 300 N force in the downward direction.*
* Again, pedants can argue that such notation can be made self-consistent. I'm teaching introductory physics, with students who still struggle with the idea that "-300 N" doesn't mean "bad 300". It's far more important to use notation that addresses the physical meaning of a quantity than notation that maybe, perhaps, with expertise, can be made mathematically reasonable.
So don't ever use negative signs with electric fields -- they're too easy to confuse with negative charges, which mean something completely different, and negative potentials, which are again different. Have students state a magnitude and direction of an electric field without negative or positive signs: "200 N/C, to the left."