# Quick Calculation of Magnetic Flux Density in Electrical Facilities
## 1 Introduction  
The influence of extremely low frequency (ELF) electromagnetic fields on the health of living beings, particularly humans, is a fact that raises interest and controversy in the scientific community and some concerns among many citizens. Possibly, the report that had the greatest worldwide impact and that raised the alarm was the so-called Karolinska report, published in 1993 by [PERSON] and [PERSON] [1], researchers at the prestigious Karolinska Institutet in Sweden. Although it is not the first scientific study on the subject [2], the large number of cases studied and the rigor of the method made it unique, and it is considered a basic reference in many countries. The report warns of a verified risk of cases of leukemia in children living next to high-voltage lines where the magnetic flux density (MFD) \(\stackrel{{\rightarrow}}{{B}}\) exceeded 0.2 uT. Other researchers have tried to verify this influence with diverse results [3; 4; 5; 6]. The same authors of the aforementioned report carried out a bibliographic review several years later [7] in which the main conclusion was that there is some evidence of a risk factor with an average value of 2 on this childhood disease that has a low incidence in the whole population. This risk is verified at locationswhere the average value of \(\overrightarrow{B}\) exceeds the threshold of 0.4 \(\upmu\)T. This conclusion led the International Commission on Non-Ionizing Radiation Protection (ICNIRP), an independent organization with a great international prestige, to publish some recommendations on the general public's exposure to electromagnetic fields [8], which were adopted by the World Health Organization (WHO) [9]. The established limits in these recommendations are based on the measurable phenomenon of induced currents in human organs. A threshold of 10 mA/m\({}^{2}\) of current density was selected since lower values do not reveal health risks for humans. With regards to occupational exposure, this has been associated with an MFD of 500 \(\upmu\)T at 50 Hz (or 420 \(\upmu\)T at 60 Hz). For the general population, a safety factor of 5 is applied, resulting in an exposure limit of 100 \(\upmu\)T at 50 Hz (or 83 \(\upmu\)T at 60 Hz). Subsequently, the Council of Europe adopted the same limits in [10], transcribed into Spanish legislation by [11]. The IEEE association also developed a standard on exposure limits to ELF magnetic fields [12]. For its part, the International Agency for Research on Cancer (IARC), based on the evidence presented in international research, classified the magnetic field of ELF as potentially carcinogenic (as opposed to the electric field) [13]. Numerous studies have tried to simulate or measure the physiological effects that ELF magnetic fields can produce inside the human body. In general, these studies analyze the induced current that the variable magnetic field can produce in various organs or tissues [14]. To date, the lack of evidence of a causal relationship between the ELF magnetic field and the development of certain diseases (such as leukemia) leads ICNIRP to consider that stricter mandatory limits cannot be established, such as 0.4 \(\upmu\)T, beyond the recommendations given by this organization. However, it warns about the possible risk and suggests considering the precautionary measures that the WHO and other agencies have proposed. Based on this precautionary principle, some countries have set MFD immersion limits below the values proposed by ICNIRP. In [10], point 4 of the preamble states: \"It is imperative to protect members of the general public within the Community against established adverse health effects that may result as a consequence of exposure to electromagnetic fields \".