Skin depth formula

This formula does not explicitly contain the temperature as a variable, but it can explain the limiting of the temperature increase at the Curie point. When the ferromagnetic conductor reaches the Curie point, the relative permeability pr of the ferromagnetic conductor suddenly drops. This generates a sudden increase in the skin depth s and therefore a decrease in 1/s and F(d,s) such that the power consumption of the conductor decreases. A further increase in temperature is therefore inhibited. Detailed graphs describing the variation of N as a function of temperature when different parameters are modified in rel. (1) are available in literature [8]. 

Application of Doll s theory permits us to derive simple expressions for the quadrature component of the magnetic field in a medium with horizontal and cylindrical interfaces, and in many cases this theory allows us to evaluate with sufficient accuracy the influence of currents, induced in the borehole and in the invasion zone as well as in other parts of the medium. It is appropriate to consider formulae based on this theory as asymptotical ones, which are valid for large values of the skin depth with respect to such parameters as ... 

Comparison of the results of calculation using exact formulae and the asymptotic eq. 4.149 shows that, if the skin depth in the borehole is greater than its radius and P2 > Pi the error in determination of the amplitude and the phase of the field by... 

We will consider the behavior of the field at the low-frequency part of the spectrum when the skin depth in both media exceeds the distance from the dipole to the interface and the probe length. In deriving asymptotic formulae we will use the approach described in chapter four, namely the interval of integration is presented as a sum of two parts, the internal part where 0 < mL < moL < 1, and the external one as m > mo. Within the external interval radicals mi and m2 can be expanded in a series by powers of k /m and k /m. For this reason the integral at the external interval is presented as a series of terms having even powers of k. Within the internal interval exponents can be expanded... 

However, conductor loss depends on the resistance (surface resistance) of the conductor. As the frequency increases, there is a tendency for the current to concentrate in the surface parts of the conductor. The part where the current flows is known as skin depth (the depth where current density falls to 1/e = 0.37 of its value at the surface), and it decreases in inverse proportion to the square root of the frequency. Surface resistance Rs is determined by skin depth d and conductor conductivity o as in the formula below. It is inversely proportional to the square root of conductor conductivity, and increases proportional to the square root of the frequency. 

To reduce conductor loss in high frequency ranges, it is necessary to take an proach that reduces conductor resistance to the minimum (refer to Chapter 1). Since the inductance of the conductor inside increases at high frequencies, current flows only near the surface of the conductor layer. The thickness of the area where the current flows is called skin depth. Figure 10-1 shows the relationship between the frequency of each type of conductor and the skin depth. The relationship with skin depth ( ) is in accordance with the formula below, and there is a tendency for the skin depth to become shallower as the frequency increases with materials that are not magnetized. 

The thickness of any planar shield can be represented in terms of skin depths to indicate the shielding potential of the material. In addition to the absorption over skin depth, significant reduction of the impinging electromagnetic field can occur through reflection from the shield surface. The formula of far-lield reflection loss for plane-wave radiation is given by Eqn (8.26) (Das et al., 2000). 

Standard skin preparation increases the depth of penetration of Jessner s solution and improves the results - at the same time as increasing the risk of complications. An allergy test is essential, especially because of the resorcinol in the formula. 

Phenol is not considered to be carcinogenic. On the contrary, long-term histological studies show that phenol (even when the formula contains croton oil) has a protective effect against skin cancers. A logical explanation of this protective effect may lie in the fact that the cells that take the brunt of UV rays are the keratinocytes closest to the stratum corneum, the ones that form, for example, the top of the dermal papillae. On the other hand, the keratinocytes that are in the lower regions of the dermal papillae are relatively protected compared with those higher up the UV photons have been partially absorbed or diffracted by the epidermal layers above them. In addition, the sebo-cytes or keratinocytes that make up the shaft of the hair are anchored more deeply in the skin, at a depth where the harmful effects of the sun are not as severe. 

Stone performed a histological study of the depth of penetration of various phenol formulas the Gordon-Baker formula at 48.5% phenol, the Verner-Dickinson formula at 67% and liquid phenol at 88%. The results, in keeping with the principles set out above, show that Baker s formula penetrates twice as deeply as Verner s and four times as deeply as liquid phenol at 88%. Although phenol is absorbed rapidly by skin tissue, only a part of it will gradually reach the innermost regions, as the skin proteins flocculate almost immediately, and this creates a physical catchment area for the phenol as well as a natural dam that stops it penetrating the deeper layers too quickly. 

For the distributed-parameter skin compartment model, the concentration Csc is calculated by discretizing the stratum corneum compartment into a set of iV -i-2 equidistant nodes and using the central difference formula. This results in the representation of the one-dimensional Fickian diffusion equation to calculate mass flux at any depth within the stratum corneum (46) ... 

If this space scale 5 is smaller than the plasma sizes, then the external fields and currents are located only on the plasma surface layer with a penetration depth 5. This effect is known as the skin effect. The boundary layer, where the external fields penetrate and where plasma currents are located, is called the skin layer. The depth of the skin layer depends on the electromagnetic field frequency (/ = co/ln) and plasma conductivity. For calculation of the skin layer depth it is convenient to use the following numeric formula ... 

A phenomenon known as the skin effect is u.sed to describe the depth of penetration of the eddy currents, which is proportional to the current frequency (/ in Hz), the electrical conductivity (rr in mhos.m) and the magnetic permeability (n in H/m) of the material tested. The standard depth of penetration (cl in m) can be calculated using the formula... 

Figure 8.1 Test peel patches on day 4, left cheek, in Fitzpatrick skin type I treated with tour formulae (1) 48% phenol. 0% croton oil (2) 35% phenol, 0.4% croton oil (3) 35% phenol, 2.2% croton oil, and (4) 35% phenol, 0% croton oil. Each formula was tested with 50, 20 or 5 rubs with small semi-diy Q-tips (cotton buds). Results showed (1) phenol Is not all-or-none (2) croton oil increases depth of injury (3) In this study there was little observable difference between 0.4% and 2.2% croton oil (4) mbbing increases depth of injury, and (5) human experimental models have inherent variables...

Chemical peels can be classified by the depth of penetration into the skin (Table 9.2). Superficial peelings (epidermis to upper papillary dermis) are the most commonly used peels in all phototypes. These agents include tretinoin 1-5%, TCA 10-35%, glycolic acid solution 30-50% or glycolic gel 70%, salicylic acid 20-30% in ethanol and Jessner s solution (Combes formula). 

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