Current

Discussion in 'Homework Help' started by Debdut, Mar 11, 2012.

  1. Debdut

    Thread Starter New Member

    Aug 26, 2011
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    Current has a direction but why it is not a vector?
     
  2. steveb

    Senior Member

    Jul 3, 2008
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    In some contexts, current can be treated as a vector, but it is better to say that current has magnitude that can be positive or negative. This makes it a scalar quantity. It some sense, the sign of the current can be interpreted as direction, for example in a circuit, but this is different than a spatial direction.

    It is a confusing and ambiguous thing. Often the world is not black and white and you need to think in shades of gray.

    Rather than a direction, you can think of current as being associated with an oriented area. Think of taking a small rectangle. This rectangle might allow charges to flow through it at a certain rate. The current divided by the area of the square is the notion of current density.

    If you have a filamentary current density traveling along a path, then one can treat this like a current vector mathematically. However, it is understood that the reality is that you have a highly confined current density.

    Usually, current density is treated as a vector, in 3D space, under the mathematics of vector calculus in electromagnetism. Integration (or adding up) of current density over an area gives current, which makes it a scalar.

    In differential geometry, current density is a little more complicated than that (it is a two-form in 3D space), but that is a subject for another day.

    http://en.wikipedia.org/wiki/Current_density
     
    Debdut likes this.
  3. Debdut

    Thread Starter New Member

    Aug 26, 2011
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    Can you tell then why we do scalar summation for current?You said that sometimes we consider it vector?But overall thanks.
     
  4. steveb

    Senior Member

    Jul 3, 2008
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    One abstract way to answer that is to say that the mathematical object that we call current is a scalar by definition. In vector calculations we take the vector current density and integrate it over area via a dot product. The area has a normal vector associated with it and the dot product of two vectors is a scalar.

    If you use the exterior calculus of differential forms, the mathematical objects are more complex, but the end result is still that current has a scalar nature to it.

    Thinking more simply. Consider that current is the time rate of change of charge as it flows through some confined area. Charge itself is not really a vector, so the time rate of change of it should not be a vector.

    But, I still caution that mathematics is quite flexible and one can still imagine current as a vector. For example, what if you have a stream of charged particles moving at a particular velocity. Velocity is a vector and you could argue that current I=qv. Since v is a vector, then a scalar q times v should be a vector. This could be a gray area in definitions, although a purist would say that the particle stream is better described by current density, which is a vector field.
     
    Last edited: Mar 15, 2012
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