What is Current? I know it is a scalar but I found something weird....

[Austin 30]

While I was going through "Introduction to Electrodynamics" by David J. Griffith I see the line "Current is a vector quantity". But we know it doesn't obey the vector algebra (addition ). Then how it can be a vector?... Please help me

 

[Ibix]

Current is the charge on a particle (a scalar) times its velocity (a vector), so is a vector. You may sum over multiple charged particles (and we often do), but the result is still a vector.

Are you thinking of circuit analysis? The laws describing current in circuits do not treat current as a vector, true. But that's because they just treat the circuit as an abstract collection of lines and junctions that current flows along - they don't explicitly model the electromagnetic interactions that make the current follow the wires. Here, Griffiths is not using such high-level abstraction.

 

[PeroK]

While I was going through "Introduction to Electrodynamics" by David J. Griffith I see the line "Current is a vector quantity". But we know it doesn't obey the vector algebra (addition ). Then how it can be a vector?... Please help me

What do you mean that it doesn't obey vector addition?

Current is a flow of charge. By definition, flow has a direction, hence is a vector.

 

[Austin 30]

What do you mean that it doesn't obey vector addition?

Current is a flow of charge. By definition, flow has a direction, hence is a vector.

No..no...the full definition of vector is ...it should follow vector algebra...and It doesn't... example suppose you have 2 wires , with angle θ then the total current in the added wire should i^2 = (i1)^2+(i2)^2+2(i1)(i2)cosθ ..but as we know it is just i1+i2

 

[DrClaude]

No..no...the full definition of vector is ...it should follow vector algebra...and It doesn't... example suppose you have 2 wires , with angle θ then the total current in the added wire should i^2 = (i1)^2+(i2)^2+2(i1)(i2)cosθ ..but as we know it is just i1+i2

Did you read @Ibix's reply?

Are you thinking of circuit analysis? The laws describing current in circuits do not treat current as a vector, true. But that's because they just treat the circuit as an abstract collection of lines and junctions that current flows along - they don't explicitly model the electromagnetic interactions that make the current follow the wires. Here, Griffiths is not using such high-level abstraction.

The wire makes the direction of the current change, so you can't blindly use vector summation in that case.

 

[Austin 30]

Current is the charge on a particle (a scalar) times its velocity (a vector), so is a vector. You may sum over multiple charged particles (and we often do), but the result is still a vector.

Are you thinking of circuit analysis? The laws describing current in circuits do not treat current as a vector, true. But that's because they just treat the circuit as an abstract collection of lines and junctions that current flows along - they don't explicitly model the electromagnetic interactions that make the current follow the wires. Here, Griffiths is not using such high-level abstraction.

Sir, can you please tell me "that's because they just treat the circuit as an abstract collection of lines " this one.. if we assume the cirvuci as collccolle of lines then how the vector is turned into scalar?...as far i know they assurm the quantity as scalar as it doesn't obey Vector addition rule.

 

[Austin 30]

Did you read @Ibix's reply?

The wire makes the direction of the current change, so you can't blindly use vector summation in that case.

Sir the in case of a planar conductor it should obey vector addition??...but practically it doesn't obey there also

 

[DrClaude]

The current inside wires is treated as a scalar because it is easier to work this way. In reality, it is a vector quantity that is always parallel to the wire, so there is not point in keeping track of the direction if it keeps changing but always follows the wire.

Take as an analogy a marble rolling in a bent tube. The velocity vector of a marble changes as it goes along the tube, but (neglecting friction), its speed is constant, so it makes sense to treat the problem using speed (a scalar) instead of velocity (a vector).

 

[Austin 30]

The current inside wires is treated as a scalar because it is easier to work this way. In reality, it is a vector quantity that is always parallel to the wire, so there is not point in keeping track of the direction if it keeps changing but always follows the wire.

Take as an analogy a marble rolling in a bent tube. The velocity vector of a marble changes as it goes along the tube, but (neglecting friction), its speed is constant, so it makes sense to treat the problem using speed (a scalar) instead of velocity (a vector).

According to the Analogy it works as there if I use 2 balls then angle between them is 0° or 180° thatst why normal scalar addition works...but in this case there is a general angle θ so it will not work

 

[DrClaude]

Here is what it looks like using your example of two wires joining into one.

 

[DrClaude]

According to the Analogy it works as there if I use 2 balls then angle between them is 0° or 180° thatst why normal scalar addition works...but in this case there is a general angle θ so it will not work

Don't take the analogy too far. It doesn't work for colliding balls.

 

[PeroK]

Sir the in case of a planar conductor it should obey vector addition??...but practically it doesn't obey there also

Well, put simply, you ain't going to get far with electromagnetism if you persist with the idea that current is a scalar!

It's like saying velocity is a scalar because you've studied some 1D problems. A circuit is, essentially, a 1D set up, where the current is constrained to a 1D path. In general, in a 3D object, the current can flow in any direction.

 

[Dale]

I must say that I disagree with my colleagues and with Griffith.

Current density is a vector, but current is a scalar. As the OP correctly points out current does not follow the rules of vector addition. Also, in circuit theory there is no space so there are no directions, so there can be no vectors for any quantities in circuit theory.

What Dr. Griffith has actually written is the current density rather than the current. The current scalar is related to the current density vector by $I=\int \mathbf{J}\cdot d\mathbf A$

 

[jbriggs444]

What Dr. Griffith has actually written is the current density rather than the current. The current scalar is related to the current density vector by $I=\int \mathbf{J}\cdot d\mathbf A$

Trying to make sure I understand what you are laying down. For you, "current" would denote the signed magnitude of the rate of flow of charge through a defined surface. Where the "surface" could be a cross-section slicing through a current-carrying wire, for instance. Or the back side of a CRT screen being bombarded by electrons. Or even the boundary enclosing a cubical volume of electrolyte (through which we would expect the net flow to be zero always).

In all cases the surface has a direction -- a front and a back (or an inside and an outside). So the current is signed. We can distinguish between +1 amp (net current flowing in the back side) and -1 amp (net current flowing in the front side).

 

[stevendaryl]

The current scalar is related to the current density vector by $I=\int \mathbf{J}\cdot d\mathbf A$

I'd call that a "pseudo-scalar", because its sign depends on a convention for which direction is considered "positive".

 

[Dale]

Trying to make sure I understand what you are laying down. For you, "current" would denote the signed magnitude of the rate of flow of charge through a defined surface. Where the "surface" could be a cross-section slicing through a current-carrying wire, for instance. Or the back side of a CRT screen being bombarded by electrons. Or even the boundary enclosing a cubical volume of electrolyte (through which we would expect the net flow to be zero always).

In all cases the surface has a direction -- a front and a back (or an inside and an outside). So the current is signed. We can distinguish between +1 amp (net current flowing in the back side) and -1 amp (net current flowing in the front side).

Yes, exactly. The vector $d\mathbf A$ has a direction and when $\mathbf J$ is in the same direction then $I$ is positive and vice versa if they are in opposite directions.

 

[PeroK]

I must say that I disagree with my colleagues and with Griffith.

Current density is a vector, but current is a scalar. As the OP correctly points out current does not follow the rules of vector addition. Also, in circuit theory there is no space so there are no directions, so there can be no vectors for any quantities in circuit theory.

What Dr. Griffith has actually written is the current density rather than the current. The current scalar is related to the current density vector by $I=\int \mathbf{J}\cdot d\mathbf A$

Interesting. Perhaps this isn't as simple as it first looks.

If current is a scalar, then current density ought to be a scalar too. Hmm?

Suppose we leave the known terminology to one side. We start with a quantity, which we simply call $\vec{J}$ and which has dimensions of charge-velocity/volume.

If we model a wire as a 3D object with uniform cross section, $A$, then we can define a quantity which we call $\vec{I}$ by:

$\vec{I} = A\vec{J}$

$\vec{I}$ has units of charge-velocity/length.

Now, Griffiths defines the current as $\vec{I}$ and you define the current as $I = |\vec{I}|$.

And everyone is happy?

PS It seems to me that $\vec{J}$ is misnamed as "current density" in either case, although more of a misnomer if current is a scalar!

 

[Dale]

Now, Griffiths defines the current as →II→\vec{I} and you define the current as I=|→I|I=|I→|I = |\vec{I}|.

Currents in my definition can be negative. This definition is strictly non negative.

 

[cosmik debris]

I'd call that a "pseudo-scalar", because its sign depends on a convention for which direction is considered "positive".

If I remember correctly, when I was at school the nomenclature for current changed. Originally termed vectors in the literature it was changed to phasor for exactly the reasons given above.

Cheers

 

[PeroK]

Currents in my definition can be negative. This definition is strictly non negative.

Yes, of course, it's $\vec{J} \cdot \vec{A}$ in your case.

 

[vanhees71]

Hm, Griffiths seems to be quite sloppy in his textbooks leading to confusion of his readers, although I consider his textbook on electrodynamics as pretty good. The quantum textbook is much worse in this respect :-(.