## 8 Surface Current, Magnetic Field, and Electric Field Analysis  
In a metallic resonator, the surface current delineates the actual current generated by the time varying electromagnetic field. This actual current produces a magnetic field, so  
Figure 10: The graph of (**a**) permittivity vs. frequency, (**b**) permeability vs. frequency, (**c**) refractive index vs. frequency, and (**d**) impedance vs. frequency.  
the changing magnetic field produces an electromotive force. [PERSON] and conventional law have proposed several equations to elucidate the relationship between surface current, E-field, and H-field through the following equations [37]:  
\[\
abla\times H=J+\frac{\partial D}{\partial t} \tag{8}\]  
\[\
abla\times E=-\frac{\partial B}{\partial t} \tag{9}\]  
where  
\[\
abla=\left[\frac{\partial}{\partial x}\frac{\partial}{\partial y}\,\ \frac{ \partial}{\partial z}\ \right] \tag{10}\]  
\[D(t)=\varepsilon(t)*E(t) \tag{11}\]  
\[B(t)=\mu(t)*H(t) \tag{12}\]  
where \(E\), \(H\), \(D\), \(B\), \(\varepsilon\), \(\mu\), and \(J\) are \(E\)-field intensities, H-field intensities, electric flux densities, magnetic flux densities, electric permittivity, magnetic permeability, and time-varying electric current density in a medium, respectively.  
Figure 11 displays the surface current, H-field, and E-field distribution of the proposed unit cell at the frequencies of 2.02, 6.985, 9.985, and 14.425 GHz.  
At a frequency of 2.02 GHz, the outer SRR provides a low impedance path, thereby creating a strong surface current, as shown in Figure 11(ai). In Figure 11(bi), a good understanding was observed between surface current and H-field distribution, which was confirmed by [PERSON]'s law (\(\int B.dl=\mu_{0}I\)). As the current increases, the intensity of the H-field also increases. Strong surface current creates a higher H-field in same place. According to [PERSON]'s law, the greater the value of the H-field in SRR, the greater value of the E-field on the other side of the SRR due to capacitive effect is shown in Figure 11(ci).  
At the resonance frequency of 6.985 GHz, the outer SRR produces a little bit of current. In the other portion, the surface current was evenly distributed, as shown in Figure 11(aii). The Coptic shape resonator also contributed less to the surface current flow due to increasing the capacitive response for split gap. On the other hand, the SRR shows a small strength of H-field; the Coptic cross shape resonator has almost no current due to the split gap and the H-field approaches zero, as shown in Figure 11(bi). Meanwhile, the split gap of the SRR and Coptic shape resonator create an additional electric field due to forming a capacitor, as indicated in Figure 11(ci).  
At a frequency of 9.985 GHz, the entire unit cell resonator, except the split gap of the SRR and Coptic shape, four cross shaped resonators, contributed most of the surface current, as indicated in Figure 11(aiii). This higher surface current creates a strong H-field through the same place of the resonator, as shown in Figure 11(biii). As shown in Figure 11(ciii), an increased E-field is observed throughout the structure at this resonance frequency, except in the resonator where the H-field is larger.  
At the resonance frequency of 14.425 GHz, lower current densities were recorded across the unit cell as the impedance increased with higher frequencies, as shown in Figure 11(aiv). From the Figure 11(biv), it can be seen that the concentration of H-field remains the same where the surface current is higher. Meanwhile, the E-field strength is high where the H-field is low as a result of creating a mutual capacitance in a metamaterial unit cell, as shown in Figure 11(civ). The scale and axis views are shown in Figure 11v for the distribution of surface current, H-field, and E-field.