Question

If electric current is assumed as vector quantity, then:
A. Charge conservation principle fails
B. Charge conservation principle does not fail
C. Coulomb's law fails
D. None of the above

Answer 1

Hint: Electric current is defined as the flow of charges per unit time. The direction of flow of current in a circuit is opposite to the direction of flow of electrons. Electric current is a scalar quantity. But, here it is assumed to be a vector quantity. So, it has to obey basic vector rules which a vector quantity obeys. This, use the mentioned principles given as the options and check whether they are satisfied or not.

Complete answer:
The above figure shows that a current carrying wire splits in two channels. Let the angle between these two channels be A.
As the wire splits, the current flowing through the wire also splits.
Let the current split into ${I}_{1}$ and ${I}_{2}$.
Now, according to the law of vector addition,
${I}^{2}= {I}_{1}^{2} +{I}_{2}^{2} + 2{I}_{1}{I}_{2}cos{A}$
$\therefore I= \sqrt {{I}_{1}^{2} +{I}_{2}^{2} + 2{I}_{1}{I}_{2}cos{A}}$
As, $-1\le cos{A}\le 1$,
${I}_{1}-{I}_{2}\le I\le {I}_{1}+{I}_{2}$
Current is the rate of flow of charge. So, if the charge Q is flowing in one second then the current in terms of charge can be written as,
${Q}_{1}-{A}_{2}\le Q\le {Q}_{1}+{Q}_{2}$
From the above equation we can say that charge entering the junction is not equal to charge leaving the junction. Thus, charge is not conserved.

So, the correct answer is “Option A”.

Note:
To solve such questions you should know the difference between scalar and a vector quantity. You should also know which basic rules these quantities obey. A scalar quantity is a quantity which only has magnitude. A vector quantity is a quantity which has both magnitude and direction. Electric current has both magnitude and direction, still it is a scale quantity. As it does not follow the vector addition rule.