Use Coulomb’s law to derive the dimension for the permittivity of free space. ​

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Use Coulomb’s law to derive the dimension for the permittivity of free space.

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Thanh Hà 3 years 2021-08-18T15:27:03+00:00 1 Answers 14 views 0

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  1. ngockhue
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    2021-08-18T15:28:21+00:00
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    Answer:

    Coulomb’s law is:

    F = \frac{1}{4*pi*e0} *(q1*q2)/r^2

    First, force has units of Newtons, the charges have units of Coulombs, and r, the distance, has units of meters, then, working only with the units we have:

    N = (1/{e0})*C^2/m^2

    then we have:

    {e0} = C^2/(m^2*N)

    And we know that N = kg*m/s^2

    then the dimensions of e0 are:

    {e0} = C^2*s^2/(m^3)

    (current square per time square over cubed distance)

    And knowing that a Faraday is:

    F = C^2*S^2/m^2

    The units of e0 are:

    {e0} = F/m.

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