# Why is an electric current a scalar

## Why is current a scalar quantity?

To be precise, current is not a vector quantity. Although the current has a certain direction and magnitude, it does not follow the law of vector addition. Let me show you

Take a look at the picture above. According to Kirchhoff's current law, the sum of the currents entering the junction should be equal to the sum of the currents exiting the junction (no charge accumulation and discharges). A current of 10 A leaves the connection point.

Now take a look at the picture below.

Here I have considered current as a vector quantity. The resulting current is less than that obtained in the previous situation. This finding gives us some implications, and I want to go over some of them. This can occur due to a build-up of charge on some parts of the conductor. This can also be due to a cargo leak. In our daily routine we use materials that are roughly ideal so that these phenomena can be neglected. In this case the difference in the situations can be seen and we cannot neglect it.

If you're not convinced, let me tell you more. In the description above (currently as a vector) I only talked about the size difference. The direction of the resulting stream (as shown) is subtle. This is because in practice we are not observing the current flowing along the direction shown above. You can argue that in the presence of the conductor, the electrons can only move inside and therefore follow the available path. You can also argue that the electric field in the conductor imposes some restrictions. I appreciate trying, but what if I remove the ladder? I also use particle accelerators that shoot proton beams while neglecting the presence of an electric field in space.

Now let me look at two beams of protons (currents), each carrying a current of 5A, as shown below. These rays are isolated and we will not consider outside influences.

Since there is no restriction on the flow of protons, the protons that meet at the junction exchange momentum and this leads to scattering (protons represented by small circles). You would have a situation where two rays create multiple rays as shown below. Our vector addition law does not say this.

I've illustrated some in the picture above. In reality, you will see chaotic movement. Representing the rays (as shown above) becomes a very difficult task because the protons do not follow a fixed path. I just showed you an unlikely but possible situation.

All of this clearly shows us that current is not a vector quantity.

Another point I want to mention is that unlike other vector quantities, current cannot be broken down into components. Current flowing in a certain direction only has an effect along the direction of flow for an infinite period of time (without external influences such as electric or magnetic fields).

### Ruslan

If a quantity is not a vector, it does not become scalar.

### Ruslan

The scalar quantity is a quantity that cannot be changed during rotations. The current is not invariant in rotations. The physical quantities can also include pseudotensors (including pseudoscalars) and even things like the sum of the tensor and pseudotensor - such quantities are definitely not among those you've listed.

### R004

Could you shed some light on the current, which is a different physical quantity than a vector?

### Ruslan

In fact, it may appear scalar depending on how you define the differential cross-section vector dEIN⃗ in the definition of the current I = ∫J.⃗dEIN⃗. If you define it to change direction under parity inversion, then I am pseudoscalar. Otherwise it is scalar. Or I can be wrong and dEIN⃗ has a clear definition.

### R004

Wikipedia speaks of a four-dimensional analogue of 'electrical current density' (a vector quantity that is known to us in our three dimensions). I am talking about electricity. I hope it's clear