I have always been a bit confused on deciding on scalar and vector quantities. Most of the time, my intuition gives me opposite to the right answer. So now I desperately want to know why power including work is a scalar quantity.

You are watching: Is power a scalar or vector  Power on its own is defined as being the rate of energy transfer, and it has no additional information as to its direction, so it is a scalar. However, there is a vectorial quantity which is related to power, known as the Poynting vector.

Given say, an electric field \$mathbfE\$ and magnetic field \$mathbf B\$, the Poynting vector is defined as,

\$\$mathbf S = frac1mu_0mathbf E imes mathbf B\$\$

which is the power in the direction of \$mathbf S\$, per unit area. Thus, if we want to know the power going through a surface \$A\$, it would be,

\$\$P = iint_A mathbf S , cdot mathrm dmathbf A.\$\$

Thus, power on its own is a scalar quantity, but we do have a notion of direction for power which is encoded in the Poynting vector, or analogues of it for other phenomena.

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answered Oct 4 "17 at 15:14 JamalSJamalS
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