Is current a vector?

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a.s.h.
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Joined: Tue Jan 28, 2014 3:50 pm

Is current a vector?

Postby a.s.h. » Mon Mar 17, 2014 8:44 pm

Hi Joe,

Electrical current seems to have a direction and magnitude. So is it a vector quantity?

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joe
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Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

Re: Is current a vector?

Postby joe » Wed Mar 19, 2014 9:47 am

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


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