Abordamos um clássico problema de Eletrostática presente em livros didáticos do Ensino Médio e Superior: o campo elétrico gerado por um excesso de cargas em uma esfera condutora. De início, analisamos especificamente o valor do campo na superfície da esfera condutora, assumindo que as cargas estão todas distribuídas exatamente nessa superfície. Em seguida, ao flexibilizar a distribuição de cargas para um modelo de distribuição uniforme numa camada esférica de pequena espessura, mostramos que as aparentes discordâncias entre os resultados apresentados na literatura não são matemáticas. Elas apenas evidenciam as limitações dos modelos adotados para representar o objeto. Palavras-chave: modelização, campo elétrico, descontinuidade.We study a classical electrostatic problem presented in highschool and university textbooks: the electric field generated by a charge excess in a spheric conductor. Firstly, we verify the field value on the surface of the conductor, assuming the singular charge distribution model. Secondly, given some flexibility to the charge distribution to a uniform density over a tiny spherical shell, we show that apparent discrepancies that are presented in literature only give evidence of the limitations of the singular model on describing of the real object. Keywords: modelling process, electric field, discontinuity. IntroduçãoO Ensino e a própria Pesquisa em Física se apoiam em modelos que visam representar objetos reais. Evidentemente, pela complexidade da realidade, essa representação tornase parcial e aproximativa, apresentando apenas aspectos relevantes (definidos pelo pesquisador) do objeto real. Assim, um mesmo objeto pode receber incontáveis modelos que, a depender da profundidade da análise, podem ser divergentes entre si [1]. Com isso em mente, uma abordagem dos conteúdos em sala de aula a partir da modelização pode aproximar o conhecimento cientifico da realidade dos estudantes. Essa análise detalhada das limitações do modelo científicoé o norte da discussão que aqui faremos em torno do problema do campo elétrico devido um condutor carregado -problema clássico da Eletrostática -, partindo da controvérsia encontrada entre os trabalhos de Salvatore e Assad, ambos publicados na Revista Brasileira de Ensino de Física [2,3].Dada uma esfera condutora de raio R e carga Q, no vácuo, mostra-se facilmente [4,5] que o campo elétrico a uma distância r = R de seu centro tem módulo dado por(1) * Endereço de correspondência: pinheiro.marcio@gmail.com.Tomando os limites laterais em torno de r = R, uma descontinuidade em E(r) se estabelece:

Aims. We attempt to identify the ionising stars and to determine the photometric distances of nine southern Galactic H ii regions.Methods. We carried out optical spectroscopy and UBV photometry of the stellar content of these objects. The distance of individual stars were obtained by spectroscopic parallax. To avoid using a fixed value for the total-to-selective extinction ratio R V , the reddening A V was determined directly by the colour-difference approach by comparing our V apparent magnitudes and the JHK magnitudes from the 2MASS survey with the intrinsic colour indices. Results. As types O or B, we classified 24 of the 31 stars for which optical spectra were obtained. In particular, we identified two new O stars, one in RCW 98 and the other in RCW 99. The values of reddening obtained correspond to a mean R V = 3.44, which is about 10% higher than the value found for field stars. For three of the H ii regions studied (Bran 186, NGC 2626, and RCW 32), the distance estimates (with errors from 25% to 50%) were based on the data obtained for only one star. For the other six objects (NGC 3503, NGC 6334, RCW 55, RCW 87, RCW 98, and RCW 99), we obtained more precise photometric distances (with a mean error of ≈18%) calculated to be the median of the parallax distances obtained for two to six different stars in each nebulae. The parallax distances of individual stars belonging to a given nebula were similar to each other, with internal errors smaller than 5%, as a consequence of the method used to derive the reddening correction A V . The distance of 1.23 ± 0.30 kpc obtained for RCW 87 disagrees with the value of 7.6 kpc previously found. Conclusions. The dispersion in individual distance estimates for stars in a given nebula can be significantly reduced by calculating the reddening A V from a comparison between the V and the 2MASS JHK magnitudes instead of using A V = R V E(B − V) with a fixed value for R V . Therefore, more precise distances can be calculated with our proposed method.

We report a study of the stellar content of the near‐infrared (NIR) cluster [DBS2003] 157 embedded in the extended H ii region GAL 331.31−00.34, which is associated with the IRAS source 16085−5138. JHK photometry was carried out in order to identify potential ionizing candidates, and the follow‐up NIR spectroscopy allowed the spectral classification of some sources, including two O‐type stars. A combination of NIR photometry and spectroscopy data was used to obtain the distance of these two stars, with the method of spectroscopic parallax: IRS 298 (O6 V, 3.35 ± 0.61 kpc) and IRS 339 (O9 V, 3.24 ± 0.56 kpc). Adopting the average distance of 3.29 ± 0.58 kpc and comparing the Lyman continuum luminosity of these stars with that required to account for the radio continuum flux of the H ii region, we conclude that these two stars are the ionizing sources of GAL 331.31−00.34. Young stellar objects (YSOs) were searched by using our NIR photometry and mid‐infrared (MIR) data from the Galactic Legacy Infrared Mid‐Plane Survey Extraordinaire (GLIMPSE) survey. The analysis of NIR and MIR colour–colour diagrams resulted in 47 YSO candidates. The GLIMPSE counterpart of IRAS 16085−5138, which presents IRAS colour indices compatible with an ultracompact H ii region, has been identified. The analysis of its spectral energy distribution between 2 and m revealed that this source shows a spectral index α= 3.6 between 2 and m, which is typical of a YSO immersed in a protostellar envelope. Lower limits to the bolometric luminosity and the mass of the embedded protostar have been estimated as L= 7.7 × 103 L⊙ and M= 10 M⊙, respectively, which correspond to a B0–B1 V zero‐age main sequence star.

The Norma section of the Milky Way is especially interesting because it crosses three spiral arms: Sagittarius-Carina, Scutum-Crux and the Norma arm itself. Distance determinations of embedded young stellar clusters can contribute to define the spiral structure in this part of the Galaxy. However, spectrophotometric distances were obtained for only a few of these clusters in Norma. We present a photometric and spectroscopic study in the NIR of the [DBS2003] 156 stellar cluster, associated with the H II region G331.1−0.5. We aim to find the ionizing sources of the H II region and determine its distance. The cluster was observed in the J, H, and K s bands and eight potential massive stars were chosen among the detected sources according to color criteria; subsequent spectroscopy of these candidates was performed with the Ohio State Infrared Imager/Spectrometer spectrograph attached to the Southern Observatory for Astrophysical Research 4.1 m telescope. We identified and classified spectroscopically four earlytype stars: IRS 176 (O8 V), IRS 308 (O-type), IRS 310 (O6 V), and IRS 71 (B1 Iab). Based on the proximity of IRS 176 and 308 with the radio continuum emission peaks and their relative positions with respect to the warm dust mid-infrared emission, we concluded that these two stars are the main ionizing sources of the H II region G331.1−0.5. The mean spectrophotometric distance of IRS 176 and 310 of 3.38±0.58 kpc is similar to that obtained in a previous work for two early-type stars of the neighbor cluster [DBS2003] 157 of 3.29±0.58 kpc. The narrow range of radial velocities of radio sources in the area of the clusters [DBS2003] 156 and 157 and their similar visual extinction indicate that these clusters are physically associated. A common distance of 3.34±0.34 kpc is derived for the system [DBS2003] 156 and 157.