Explain why electricity is a scalar quantity in detail.
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Is current a scalar or a vector quantity?
Originally Answered: What is electric current, scalar or vector?
Electrical current is a scalar quantity. The reason why it is often considered vector is fairly simple:
Electrical current is defined by a formula:
I=nAve
Electricity is like water. Imagine that a wire is a pipe with lots of ‘water’ particles flowing through it (electrons). Current is a measure of how much charge flows past a point in a second. So we measure how many electrons pass one point in a second and then work out how much charge there is by multiplying the charge carried by one electron by however many electrons pass that point.
In our formula
I = Electrical Current, n = Number of electrons per unit volume (electron density), A = Cross-Sectional Area of wire, v = Average electron velocity,
e = Charge of an electron (1.6∗10−19)
(Quite proud of my 10 minute paint drawing there!)
This cylinder represents the electrons that have passed a fixed point in one second. The length of the cylinder is v, the distance traveled in one second. You can see the cross sectional area and the dots represent electrons. To work out the current, we multiply the area by the length (volume of a cylinder) then multiply that by the n-number (density) to work out how many electrons are in there. Then finally, we multiply that by the charge, et voila we have the current (amount of charge passing a point in one second).
So how does this prove it’s a vector you ask?
v.
Velocity is a vector it is positive or negative depending on direction. The electrons can flow either way through a wire depending which way around your positive and negative are. A scalar quantity doesn’t have direction, but current does because you can change the direction of those little electrons in the wire and thus the direction the charge is moving!
However, Physics and electricity isn’t all that simple!
Take Kirchoff’s Law for example:
Dr Gustav Kirchoff was a pretty clever bloke and decided he was going to make a law of Physics for his Ph.D and came up with this:
If 2 currents flow into a point like so, then the resulting will have to be be equal to the input. Makes sense, right? Doesn’t make current a scalar yet. But what if this happened?
Now, I’ve sort of proven that Current is a vector, right? Well, then we should be able to prove the current is still the same. We can do this through vector addition.
So hang on, what’s happened here? √50 is approximately 7.07A, not 10A as it should be? To be a vector, a quantity must follow the rule of vector addition, which current doesn’t. Now because it is disqualified from being a vector, the scientific community has classified it as a scalar.
This is further demonstrated by proton beams (I won’t go into it, but protons also carry charge and therefore a proton beam has current). In the real world when you fire two proton beams together, they scatter like below:
This definitely does not match up to the laws of vector addition! So current is definitely not a vector. But, it does have direction? But, apparently that doesn’t disqualify it from being a scalar…
Maybe we should just realise that all quantities are unique and stop trying to put them into boxes!
Current is a scalar because the science says so.
hope it helps
Originally Answered: What is electric current, scalar or vector?
Electrical current is a scalar quantity. The reason why it is often considered vector is fairly simple:
Electrical current is defined by a formula:
I=nAve
Electricity is like water. Imagine that a wire is a pipe with lots of ‘water’ particles flowing through it (electrons). Current is a measure of how much charge flows past a point in a second. So we measure how many electrons pass one point in a second and then work out how much charge there is by multiplying the charge carried by one electron by however many electrons pass that point.
In our formula
I = Electrical Current, n = Number of electrons per unit volume (electron density), A = Cross-Sectional Area of wire, v = Average electron velocity,
e = Charge of an electron (1.6∗10−19)
(Quite proud of my 10 minute paint drawing there!)
This cylinder represents the electrons that have passed a fixed point in one second. The length of the cylinder is v, the distance traveled in one second. You can see the cross sectional area and the dots represent electrons. To work out the current, we multiply the area by the length (volume of a cylinder) then multiply that by the n-number (density) to work out how many electrons are in there. Then finally, we multiply that by the charge, et voila we have the current (amount of charge passing a point in one second).
So how does this prove it’s a vector you ask?
v.
Velocity is a vector it is positive or negative depending on direction. The electrons can flow either way through a wire depending which way around your positive and negative are. A scalar quantity doesn’t have direction, but current does because you can change the direction of those little electrons in the wire and thus the direction the charge is moving!
However, Physics and electricity isn’t all that simple!
Take Kirchoff’s Law for example:
Dr Gustav Kirchoff was a pretty clever bloke and decided he was going to make a law of Physics for his Ph.D and came up with this:
If 2 currents flow into a point like so, then the resulting will have to be be equal to the input. Makes sense, right? Doesn’t make current a scalar yet. But what if this happened?
Now, I’ve sort of proven that Current is a vector, right? Well, then we should be able to prove the current is still the same. We can do this through vector addition.
So hang on, what’s happened here? √50 is approximately 7.07A, not 10A as it should be? To be a vector, a quantity must follow the rule of vector addition, which current doesn’t. Now because it is disqualified from being a vector, the scientific community has classified it as a scalar.
This is further demonstrated by proton beams (I won’t go into it, but protons also carry charge and therefore a proton beam has current). In the real world when you fire two proton beams together, they scatter like below:
This definitely does not match up to the laws of vector addition! So current is definitely not a vector. But, it does have direction? But, apparently that doesn’t disqualify it from being a scalar…
Maybe we should just realise that all quantities are unique and stop trying to put them into boxes!
Current is a scalar because the science says so.
hope it helps
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