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Question

# In spite of having both magnitude and direction why is electric current a scalar quantity not a vector quantity.

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Solution

## First let us define a vector! A physical quantity having both magnitude and a specific direction is a vector quantity. Is that all? No! This definition is incomplete! A vector quantity also follows the triangle law of vector addition. Let us understand that with a simple example! Say you are at home right now! From there you go to school and then you go shopping to some supermarket. So now you have moved from points A to B to C! Now when you come back home again, what is your net displacement? Its zero, because in the real sense of the word displacement, you went nowhere! You are still at your initial position! So now, net result along the path A-B-C-A is zero! This is the triangle law of vector addition! Now consider a triangular loop in an electric circuit with vertices A,B and C. The current flows from A→ B, B→C and C→A. Now had current been a vector quantity, following the triangle law of vector addition, the net current in the loop should have been zero! But that is not the case, right? You wont be having a very pleasant experience if you touch an exposed high current loop :P So that is why, electric current is a scalar quantity!

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