(Solved): 1-1. Gaussian units are based on three fundamental units: the centimeter, gram, and second. Show t ...

1-1. Gaussian units are based on three fundamental units: the centimeter, gram, and second. Show that the Gaussian unit of electric charge (the esu or electrostatic unit) is equivalent to dyne \( { }^{1 / 2}-\mathrm{cm} \equiv \mathrm{cm}^{3 / 2}-\mathrm{g}^{1 / 2}-\mathrm{s}^{-1} \). Show that the unit of capacitance is the centimeter and the unit of conductivity is the reciprocal second. SI units are based on four fundamental units: the meter, kilogram, second, and ampere. Thus the SI unit of charge (the coulomb) is \( \mathrm{C} \equiv \mathrm{A} \)-s. Show that the units of \( \epsilon_{0} \) are farad/meter \( \equiv \mathrm{m}^{-3}-\mathrm{kg}^{-1}- \) \( s^{4}-A^{2} \)