According to the definition of a Scalar quantity that i have read in class 9 is that ''those quantities which has only magnitude but no direction is known as a scalar quantity''…..But in class 10 i read that charges need to flow in a particular direction in order to form a electric current……From this argument we can conclude that a current has a specified directions which denies the definition of being a scalar quantity……
[Physics] Is electric current a scalar quantity
electric-currentelectricity
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"...direction of current does not depend upon the direction..."
This strikes me as a particularly poorly worded explanation. I might even go as far as to say that it's outright incorrect. There are two equally valid ways to explain why current is a scalar quantity, and not a vector quantity despite the fact that it does move in a particular direction:
Current is only measured as the amount of charge passing through a particular cross sectional area. Mathematically this is represented by the following equation: $$I=\int{\int_S{\vec{J}\cdot \hat{n}dA}}$$
where $\vec{J}$ is the current density.
Current is the derivative of charge with respect to time. In other words, it's the amount of charge passing through a cross sectional area at any given time, or the amount of charge leaving or entering a particular enclosed area. This is mathematically expressed as $$I=\frac{dq}{dt}$$
Again, a scalar quantity. When measuring a current, there could be several different charge sources flowing in various different directions. Current only measures the net amount of these charges that flows through an area at any given time. Depending on the direction the charge flow is moving, it may contribute more or less to the overall current through the area. When direction is important, current density is normally the quantity considered.
To be precise, current is not a vector quantity. Although current has a specific direction and magnitude, it does not obey the law of vector addition. Let me show you.
Take a look at the above picture. According to Kirchhoff's current law, the sum of the currents entering the junction should be equal to sum of the currents leaving the junction (no charge accumulation and discharges). So, a current of 10 A leaves the junction.
Now take a look at the picture below.
Here, I have considered current to be a vector quantity. The resultant current is less than that obtained in the previous situation. This result gives us a few implications and I would like to go through some of them. This could take place due to charge accumulation at some parts of the conductor. This could also take place due to charge leakage. In our daily routine, we use materials that are approximately ideal and so these phenomena can be neglected. In this case, the difference in the situations is distinguishable and we cannot neglect it.
If you are not convinced, let me tell you more. In the above description (current as a vector), I have talked about the difference in magnitudes alone. The direction of the resultant current (as shown) is subtle. That's because in practical reality, we do not observe the current flowing along the direction shown above. You may argue that in the presence of the conductor, the electrons are restricted to move along the inside and hence it follows the available path. You may also argue that the electric field inside the conductor will impose a few restrictions. I appreciate the try but what if I remove the conductors? And I also incorporate particle accelerators that say shoot out proton beams thereby, neglecting the presence of an electric field in space.
Let me now consider two proton beams (currents), each carrying a current of 5 A as shown below. These beams are isolated and we shall not include any external influences.
Now that there is no restriction to the flow of protons, the protons meeting at the junction will exchange momentum and this will result in scattering (protons represented by small circles). You would have a situation where two beams give rise to several beams as shown below. Our vector addition law does not say this.
I have represented a few in the picture above. In reality, one will observe a chaotic motion. Representation of the beams (as shown right above) will become a very difficult task because the protons do not follow a fixed path. I have just shown you an unlikely, but a possible situation.
All this clearly tells us that current is not a vector quantity.
Another point I would like to mention is, current cannot be resolved into components unlike other vector quantities. Current flowing in a particular direction will always have an effect along the direction of flow alone over an infinite period of time (excluding external influences such as electric or magnetic fields).
Best Answer
That definition of a vector quantity is a little too simple. It needs to not only have direction, but the directions need to add depending on the angles between them in a specific way to give an overall equivalent quantity.
Current in a circuit isn't really a vector quantity, it has direction but that is equivalent to just the sign of the current. You can have a positive current going in one direction and a negative current in the other - they will still add but not in a vector sense.
Perhaps there needs to be a 3rd term in between scalar and vector.