# Current in a strip - Scalar or vector [duplicate]

In certain books like David Griffiths electrodynamics , he treats current as a vector in some places. Moreover certain problems like current in a strip are often dealt with by taking current components. I am having a difficult time understanding this. After going through books and dealing with problems,i think that when current flows in a wire, of negligible dimensions, it is bound to flow along a line, so we treat it as scalar. But when we talk about current in a strip or in a volume, we can take components of current.Is it so?

• Yes, indeed I think so. Jul 8 '14 at 6:41

## 2 Answers

The reason that you typically think of it as a scalar, is because we confine the current to travelling along one path ( the wire ). This is clearly a special case. Why? Because we have a wire that predefines the path of the electricity for us. For more general situations, we don't assume a particular path, and this lets us apply vector analysis to the situation. This is because charges can generally flow in arbitrary directions. Intuitive notions of flow should tell you that we can think of flow mathematically as something passing through something as time passes. In symbols $$I = \frac{dQ}{dt}$$ This says that current is the charge, $Q$, passing through some surface area over some time. This surface area is what encodes the information for a path and where we can turn from a scalar definition to a vector definition: $$I = \int\vec{J} \cdot d\vec{A}$$ This is just another definition of charge flow, but for arbitrary paths. The aforementioned surface area, is the cross sectional area of the path the charge takes, $d\vec{A}$, and $\vec{J}$ is what is termed the current density, ie the amount of charge per cross sectional area. This is in units of $\frac{C}{m^n}$, where $n$ is the number of spatial dimensions we want to take.

Flow is a good word. Current in a sheet is described as flow, which is the same as a field and that means in general, partial DEQs. When constrained to a wire current is like water in a pipe. You don't worry about a vector field unless you get into turbulence or some other complication. The rate alone (scalar) is good enough for a lot of problems.

Griffith's book is good. You might notice that he chooses his questions very carefully. If you don't get rattled, you can do every problem in the book without putting pencil to paper.

• Sir, that means in such cases it would be better just to talk in terms of current density vector. And can you suggest any other book or links that would help through topics like these? Jul 8 '14 at 7:00
• If you are doing an E&M course, "Div Grad Curl and All That" by Schey can't hurt. Get a used 3rd edition. The 4th is expensive and uses non-physics conventions for spherical coordinates. 3rd is OK. Also Stanford has Leonard Susskind's E&M lectures online. He uses a mature sort of high level view of things in his lectures that you might find enlightening. Check other free lecture series from MIT, etc. Jul 8 '14 at 19:09