Current has a direction but is called a scalar. Which quantities are really vectors, then?

7 answers & replies

• [+][–]Arjun Nair12thSample· 1mo ago

  A vector isn't just "magnitude plus direction". It must also obey the vector addition laws (triangle/parallelogram law). Current has direction along the wire but when two currents meet at a junction we add them algebraically, e.g., $I_1 + I_2$, not by parallelogram. So current is a scalar. Same with pressure, it acts normal to a surface but isn't added by the parallelogram law (the force is the vector, pressure = force per unit area is a scalar).

  Finite rotation (angular displacement) doesn't follow commutative addition: rotate 90° about x then 90° about y is not the same as the other order. So it's not a vector. Only infinitesimal rotation is.

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  • [+][–]Diya Menon11thSample· 1mo agoAuthor

    The junction rule hook is perfect, I'll remember "currents add like numbers at a junction, not like arrows". Thanks Arjun, and Harsh for the 1-7 range! Also 4N 3N 5N is a classic 😂

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• [+][–]Harsh Gupta12thSample· 1mo ago

  For 3 N and 4 N: max when parallel, $3+4=7$ N. Min when antiparallel, $4-3=1$ N. At 90° it's the 3-4-5 triangle, resultant 5 N. So the answer is "anything between 1 and 7", and 5 is the famous middle one. Your 7 is the maximum only.

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• [+][–]Tushar PawarDropperSample· 1mo ago

  Quick list for revision.

  Scalars: mass, time, speed, distance, work, energy, power, current, pressure, charge, temperature, density, potential.

  Vectors: displacement, velocity, acceleration, force, momentum, torque, impulse, electric field, magnetic field, angular velocity (as pseudo vector), area vector.

  Physicists would also say angular velocity and torque are "axial vectors". For NEET, vector is enough.

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• [+][–]Ishita GoyalDropperSample· 1mo ago

  I think work is a vector because $W = \vec{F}\cdot\vec{d}$ and F, d are both vectors, so W should also be a vector.

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  • [+][–]Meera Patel11thSample· 1mo ago

    Ishita, the dot product of two vectors is a scalar: $\vec{A}\cdot\vec{B}=AB\cos\theta$, just a number with no direction. That's why work, power ($\vec F\cdot\vec v$) and flux are scalars. The cross product $\vec A\times\vec B$ is a vector, like torque $\vec r\times\vec F$ and angular momentum.

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    • [+][–]Ishita GoyalDropperSample· 1mo ago

      Ah yes, dot gives a number, cross gives a vector. I mixed the idea of the product being "made of vectors" with the product being a vector. Thanks Meera.

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