## Is current a vector?

A forum designed mainly for high school physics students in New South Wales, Australia.
a.s.h.
Posts: 110
Joined: Tue Jan 28, 2014 3:50 pm

### Is current a vector?

Hi Joe,

Electrical current seems to have a direction and magnitude. So is it a vector quantity?
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Is current a vector?

The normal convention for a current that stays in a quasi-one dimensional conductor such as a wire is
• treat the current as a scalar, which is conserved along the wire
• treat the local direction of the wire as a vector.
So, for instance, we write the magnetic force on a small section of wire dl carrying current i as
dF = i dl X B
Because of conservation of current, and the fact that the wire is usually bent, it's convenient to have i as a scalar, so it can have the same value around the circuit.

When we are not in a 1D conductor, then we need to use current density, to allow for variation in space. So in that case, the current density (symbol J ) is a vector.

Joe