We Shouldn’t Avoid the Unit Vector in Introductory Physics

Rhett Allain
10 min readJun 7, 2021
Photo: Rhett Allain. Unit Vectors

There is a problem with many of the algebra-based physics textbooks (and courses) — they avoid unit vectors and maybe they shouldn’t.

Oh, what is a unit vector? How about I start with a physics problem so you can see why we need unit vectors. Don’t worry, I’m going to still give my full explanation of unit vectors.

One of the first topics in the second semester of physics is that of electric fields. If you have a positive point charge, the electric field would look something like this.

The electric field is a vector that points directly away from a positive point charge. Although it’s a vector, most physics textbooks use the following equation for the electric field due to a point charge.

Yes, this is a scalar equation. I’m using k as the Coulomb constant (9 x 10⁹ N*m²/C²), q is the value of the charge and r is the distance from the charge to where you want to find the magnitude of the electric field.

Why is it a scalar equation if the electric field is a vector? I guess it’s just easier to do that. I mean, there’s really no way to write an expression for the electric field…

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Rhett Allain

Physics faculty, science blogger of all things geek. Technical Consultant for CBS MacGyver and MythBusters. WIRED blogger.