# Explain how would the energy conservation law fail if electric current is assumed as a vector quantity?

### 1 Answer | Add Yours

Perhaps you need to double check the question? Or provide greater context?

The fact of the matter is that electric current IS a vector quantity, and the energy conservation law does NOT fail. So some added detail is needed to answer your question.

Current is a vector quantity because it is made up of moving charges; the charges are moving in some direction; direction + quantity = vector quantity.

Consider the energy conservation law written in the form of Poynting's theorem:

du/dt = -∇·**S** - **J** · **E** ( · is the dot product )

Here, **J** is the current density vector; note that **I**, the current vector, is q**J**. So **I**, even as a vector, satisfies the conservation of energy. Note that current is always a vector, even if it is all flowing in only one direction.