[NOTES/EM-01013] SI System of Units

Basic SI Units

In electromagnetic theory, in addition to the standard three units, kilogram, meter and second,  a fourth unit is included. This fourth unit can be taken as the unit of charge, or of current, or of the potential difference. These units are
Unit of charge = coulomb
Unit of current = coulomb/seconds = ampere
Unit of potential difference, e.m.f. = volt
Units of all expressions can be written down in terms of four basic units kilogram, meter, sec and ampere.For ease of reference, we list units and dimensions of these and  other important quantities appearing in electromagnetic theory in the Table  in the next section.

Units and dimensions of frequently used quantities

For purposes of use in electromagnetic theory we will use ampere (A) along with the MKS units as base units. Units and dimensions of other quantities  are as follows.

$$
\begin{array}{|p{3cm}|l|ll|}
\hline &&& \\[-1.5mm]
\text{Quantity }& \text{SI unit}&  \text{Dimension}
\\[1.5mm]\hline &&&\\[-1.5mm]
\text{Potential} &  \text{V}&  \text{N/(C.m)}
\\[1.5mm]\hline &&&\\[-1.5mm]
\text{Charge density} \rho & \text{C/m\(^3\)} &
\text{A.s /m\(^3\)}
\\[1.5mm]\hline &&&\\[-1.5mm]
\text{Current density} \vec J & \text{A/m}^2 &
\text{A.m}^{-2}
\\[1.5mm]\hline &&&\\[-1.5mm]
 \text{Electric Field} \vec E & \text{N/C}, \text{V/m} &\text{kg. m. A}^{-1}. \text{s}^{-3}
\\[1.5mm]\hline &&&\\[-1.5mm]
  \text{Electric Flux} & V.m &\text{kg. m\(^3\). A\(^{-1}\). s\(^{-3}\)}\\[1.5mm]\hline &&&\\[-1.5mm]
 \text{Magnetic Induction}\vec B & \text{J. s/(C. m\(^2\))} & \text{kg. s\(^{-2}\).A\(^{-1}\)}\\[1.5mm]\hline &&&\\[-1.5mm]
 \text{Magnetic Flux} & \text{J. s/C} &\text{kg. m\(^2\).s\(^{-2}\).A\(^{-1}\)}\\[1.5mm]\hline &&&
                   \\[-1.5mm]
\text{Magnetic Field} \vec H & A/m & \text{A/m}& \\[1.5mm]\hline &&&\\
\text{Displacement Vector} \vec D & \text{C/m\(^2\)}&                                            
    \text{A/m\(^2\). s}       
    \\[1.5mm]\hline &&&\\
\text{Capacitance} &\text{C/V} &\text{kg\(^{-1}\).m\(^{-2}\).s\(^4\).A\(^2\)}\\[1.5mm]\hline &&&\\[-1.5mm]
\text{Inductance} &  \text{Wb/A} &\text{kg.m\(^2\).s\(^{-2}\).A^\(^{-2}\)}
\\[1.5mm]\hline
\end{array}$$

Units with special names

It will be seen from the above table that the units of certain physical quantities, for example flux, inductance etc, have been given special names. These units are called 'derived units'. The derived units can be expressed in terms of SI units, using the defining equations of the corresponding quantities. In  Table 3 below we list some derived units for some important quantities and their defining equations.