Hi Joe,

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

## Is current a vector?

### 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

• 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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