## 6 Electromagnetic Mass  
The second term of the effective mass depends on the so-called electrostatic energy \(U_{es}\). \(U_{es}\) denotes the formation energy of the droplet, i.e., the energy that must be expended if all the charge elements were brought together from a large distance, against the mutual repulsion forces. According to electrostatic theory [1]:  
\[U_{es}=\ \frac{1}{2}\ \iiint\limits_{droplet}\sigma.\ \Phi_{d.static}\ dx.dy.dz \tag{3}\]  
where \(\sigma\) denotes the charge density, and \(\Phi_{d.static}\) the electrostatic potential. The evaluation of \(U_{es}\) shows for the droplet [7]:  
\[U_{es}(s)=\ \frac{1}{2}\ \frac{q^{2}}{4\pi\epsilon_{0}}\ \frac{1}{s}\ \alpha \tag{4}\]  
where \(q\) is the total charge of the droplet, and the non-dimensional factor \(\alpha\) is a constant of the order \(O(1)\) depending on how the charge density varies throughout the droplet. In the present theory, no assumptions have been made as to the distribution of the charge density. The part of the inertial mass that is associated with electrical charges was in [PERSON]'s time baptised the \"electromagnetic mass\" \(m_{em}\). In the case of the droplet model, its value, in view of Equations (2) and (4), is:  
\[m_{em}(s)=\ 2\ \frac{U_{es}(s)}{c^{2}}=\frac{1}{c^{2}}\ \frac{q^{2}}{4\pi \epsilon_{0}}\ \frac{1}{s}\ \alpha\ \ \ \ \ ( droplet\ model) \tag{5}\]  
In [PERSON]'s electron theory, a similar inertial term occurs, where the fixed radius of the sphere replaces the variable length \(s\) in Equation (5), and \(\alpha=\frac{2}{3}\ ([PERSON]\ model)\). For his relativistically rigid, spherical shell model of electrons, he found \(m_{em}=\ \frac{4}{3}\ \frac{U_{L}}{c^{2}}\), which at the time caused some concern because it clearly does not conform to the relativistic relation between mass and energy. For other distributions of the charge, the factor \(\alpha\) will be different, but, because of its role as non-dimensional \"form-factor\", \(\alpha\) is in general expected to have a value of the order \(O(1)\). **7. [PERSON]'s Binding Energy**  
[PERSON] [10] requires that the above expressions are in agreement with \(E=mc^{2}\), when \(m\) is taken as the total mass \(m_{bare}+2\ \frac{U_{L}\left(s_{equ}\right)}{c^{2}}\), and if \(E\) equals the electrostatic energy (the energy of formation) \(U_{es}\big{(}s_{equ}\big{)}\). The condition that \(s\) must be taken equal to the static equilibrium length, i.e., \(s=s_{equ}\), has been added by the present author because [PERSON] does not consider deformable configurations. By \"static equilibrium length\" \(s=s_{equ}\) is meant that the velocity \(v_{m}=0\) and that there are no external squeezing forces. Under these conditions the electrostatic explosion tendency is balanced by the squeezing due to the surface tension. [PERSON]'s conclusion is that one can satisfy the relativity requirement if \(m_{bare}<0\):  
\[m_{bare}=\ -\ \frac{U_{es}\big{(}s_{equ}\big{)}}{c^{2}}=\ -\ \frac{1}{2}\ m_{em}\big{(}s_{equ}\big{)} \tag{6}\]  
The total effective mass \(m_{bare}+2\ \frac{U_{es}\big{(}s_{equ}\big{)}}{c^{2}}\) is always positive, but \(m_{bare}\) indicates a mass deficit in this positive sum. Such a mass deficit must be associated with the binding energy that is present in a charge distribution with cohesion, as opposed to a loose collection of charge elements kept together by a distribution of forces. The interpretation based on binding energy is in agreement with [PERSON]'s analysis [9] of [PERSON]'s model, where [PERSON] came to the same conclusion, viz. that the spherical shell model of [PERSON] can only be in agreement with relativity theory when the binding forces between the shell of charges and the core of insulator material are taken into account. The effective mass in Equation (2) may thus alternatively be written:  
\[m_{bare}+2\ \frac{U_{es}(s)}{c^{2}}=\ -\frac{1}{2}m_{em}\big{(}s_{equ}\big{)} +\ m_{em}(s) \tag{7}\]  
Whereas the mass of the droplet under static equilibrium conditions equals:  
\[m_{equ}=\frac{1}{2}m_{em}\big{(}s_{equ}\big{)} \tag{8}\]  
**8.