# Can scalar quantities have a direction?

Current is a scalar yet it has direction. But ideally, only vectors should possess a sense of direction. Does this mean that even scalars can possess a sense of direction? If yes, can someone give me more examples of scalars with a directional sense?

Currents do not have direction. They only have a magnitude (thought they can be negative, since charge can be negative).

However, current density is a vector quantity. It’s related to the amount of current cutting some small vector at any given point. Since the area element of a surface is a vector, this is clearly a vector quantity. The current is recovered by taking the flux of the current density over some closed surface.

Current density has direction, and magnitude, and is invariant under coordinate transforms (under a change of basis, its still the same vector). When people talk about the “direction” of a current, people are strictly speaking about the direction of the current density.So,scalars don't have direction.

Hope this helps.

• The components of current density do change under coordinate transformations (like rotation), so I wouldn't call it invariant. But otherwise this is well explained. – David Z Jul 2 '17 at 6:23
• current does have a direction, which is along the wire; because it flows along the wire it is often not indicated but it has a direction nevertheless. You correctly point out that the current density is a vector; the current is just the integral of the current density, so must be a vector also. – ZeroTheHero Jul 2 '17 at 9:42

A current in a wire does have a direction. A current in a wire also has another property, current, which is a scalar. These are separate properties. Current is not a vector.

Each molecule of air in the room has momentum and kinetic energy. Both of these arise because the molecule is moving in a direction.

Momentum is a vector. Direction is an essential part of momentum. The total momentum of air is the vector sum of the individual momenta. It adds to 0.

Direction is not part of kinetic energy. The internal energy of the air in the room is the scalar sum of the kinetic energies of the molecules. It does not add to 0.

Even though an individual molecule has a velocity that is tied to its kinetic energy, air does not have a direction associated with its internal energy.

Think about it this way - the direction of current is defined relative to some object. Current in a wire is obviously a scalar, and it has to be one, since it does not obey the laws of vector addition.

Maybe, for example, along the wire of a circuit, which is 1-D, we can treat current as a vector, as in 1-D, vectors are indistinguishable from scalars. (Until you're moving in one direction, it's fine. The moment you have two or more directions, it becomes a problem, with vectors and scalars not being the same)