Why are some quantities vectors while others aren't? For example, we can calculate both current and current density, but why do we only consider current density to be a vector and current a scalar quantity? Is it a purely arbitrary convention or is it something more mathematically fundamental? I understand vectors like forces and displacement have directions and magnitudes associated with them, but I don't quite understand why we don't do the same thing for quantities like current? Is it to simplify equations only?
Current is a vector. The difference between current and current density is the dimensions of the vector. Current density is current per cross sectional area, or number of charges moving through a volume, while current is descriptive of charges moving along a line.