Why is current-density a vector?

Asked Mar 05 '19 at 13:47

Active Mar 05 '19 at 13:58

Viewed 57 times

I was told that current has a direction but does not follow vector-laws, so it is a scalar quantity. That's okay. I thought it through Kirchoff's junction law: assume two currents joining at 90 deg, but they will not add vectorially, but algebraically.

Now, I am told that current density is a vector quantity. Solving for this, two current densities maybe added at 90 deg or 45 deg they will definitely give same result and will definitely not add vectorially.

So, why is current-density considered as vector?

$$i = j A$$ $i$ is current, $j$ is current-density, and $A$ is the area of cross-section

edited Mar 05 '19 at 13:58

asked Mar 05 '19 at 13:47

PranshuKhandal

See also https://physics.stackexchange.com/q/90995/25301 – Kyle Kanos Mar 05 '19 at 14:02
Dividing scalar by scalar doesn't yield vector, I don't really know nor understand what's going on. I don't think I can be of any help to you at the moment, but if I ever find anything soon, I'll post. Good luck pal. – TechDroid Mar 05 '19 at 14:11
1

@TechDroid thnx for help :) but as much i know, cross-section area is vector quantity.. – PranshuKhandal Mar 05 '19 at 14:13
That shows how much more I need to learn. You're welcome by the way. But what's the direction element of cross-section area? – TechDroid Mar 05 '19 at 14:20
@TechDroid perpendicular to the surface – PranshuKhandal Mar 05 '19 at 14:21
@TechDroid you can have 2 directions for each surface, but there are conventions for different cases – PranshuKhandal Mar 05 '19 at 14:22
@TechDroid you can understand it like this, a rectangle with sides as l vector and b vector has area l × b (vector product) or b × l – PranshuKhandal Mar 05 '19 at 14:24
That's just not in my sphere of thinking at all. Thanks. – TechDroid Mar 05 '19 at 14:28
@TechDroid try this, this is fascinating to learn, it also confused me when i learned them first in gauss's law httpss://physics.stackexchange.com/q/14165/221932 – PranshuKhandal Mar 05 '19 at 14:37

Why is current-density a vector?

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