I wouldn't be surprised to see mass being defined to be a vector some place where it makes sense in the given context.
Then, why would you be surprised to see mass defined a vector under some special context?
I don't think there is any definitive criterion to define some quantity as a vector or scalar.
I wouldn't be surprised to see mass being defined to be a vector some place where it makes sense in the given context.
Electric current, i, is a scalar quantity but still it is assigned positive and negative directions in circuits. Likewise, there are numerous other quantities which are scalar but still are assigned negative and positive values such as temperature. In plain words, if quantities like electric current and temperature can be assigned positive and negative values then why can't they called vector quantities? Actually, I'm confused by the fact that I relate negative and positive signs with directions. Perhaps, negative sign with quantities such as current and temperature only indicates that they have a value lower than some set standard reference value such as '0'. Please help me with it. Thank you.
I would say that is correct, and this is very close to the concept of current density. Current density is an idea related to continuous charge distributions, but the reality is that current is always discrete. Hence, an electron could be assigned a current directly with it's velocity vector (i.e. I=ev, where I is current vector, e is electron scalar charge and v is the velocity vector of the electron).I think as far as electron current is concerned (which arguably is different from 'simple' electric current), it could be considered as a vector quantity under special circumstances. For instance, if we take the motion of electrons (i.e. electron current) toward the right of screen as positive and toward the left as negative. In this case electron current has both magnitude and direction.
Electric current, i, is a scalar quantity but still it is assigned positive and negative directions in circuits. Likewise, there are numerous other quantities which are scalar but still are assigned negative and positive values such as temperature. In plain words, if quantities like electric current and temperature can be assigned positive and negative values then why can't they called vector quantities? Actually, I'm confused by the fact that I relate negative and positive signs with directions. Perhaps, negative sign with quantities such as current and temperature only indicates that they have a value lower than some set standard reference value such as '0'. Please help me with it. Thank you.
PG,
Any current, whether electrical or not, is a spacial vector quantity. Current has magnitude and direction. .
Ratch
I disagree that any current is a vector.
However, in EM theory we can define current to be the surface integral of current density, and in that case it becomes a scalar quantity defined relative to the established perimeter and orientation of the surface.
There are two two ways I can answer that: one based on the math and the other based on the physical.Why does adding up all the current differentials by integration to get a total current change it into a scalar? The total current still has a direction and magnitude.
Ratch
In the mathematical formulation of Amperes law we integrate both current density and displacement current over any surface bounded by a particular oriented boundary. In vector notation this amounts to integrating the dot product of the current densities with the normal to the surface element. Since dot product of two vectors makes a scalar, we are integrating over a scalar function. Hence, the math makes it clear that current, defined in this way is a scalar.
The physical reason is that current is just a measure of rate of charges that flow through a defined orifice. Whether the charges are directed perpendicular to the orifice or obliquely, is not relevant. Only whether the net is in or out has meaning, which relates to sign and orientation of the orifice.
I disagree that any current is a vector.
However, I hate rigor and being overly zealous with definitions, which is why I'm more flexible and open. All I said is that i disagree that any current is a vector, which only requires that I find one example where current is not a vector. Since every text book says current is a scalar, I will leave it to others to find one example to prove my point. I can think of many cases where the idea of current having a clear direction is completely untenable.
So, I'd like to make a comment here before hearing from PG and before (possibly) going into clearer descriptions. It is well known that current is a scalar quantity. Every text book says this and any online search will confirm this. Despite my absolute confidence in this known and excepted science, I was open minded enough to see and acknowledge that we often treat current as a vector entity. My contention is that we do that by simplifying current density, which is certainly representable as a vector (it's really a 2-form however from a strict geometrical perspective). However, current is not the same as current density, so really current is always a scalar, if we want to be rigorous.
However, I hate rigor and being overly zealous with definitions, which is why I'm more flexible and open. All I said is that i disagree that any current is a vector, which only requires that I find one example where current is not a vector. Since every text book says current is a scalar, I will leave it to others to find one example to prove my point. I can think of many cases where the idea of current having a clear direction is completely untenable.
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