c!!trTroo\ g.ii E 6!H d E E€ c. - P qn F >,>, o H ! sgE E E X* qotr E G' =,= F.9 '..: E sE'H'E* 3 E gIa.=i s. ao { 86: H9 I ?= o r- J S;89E5 I +. N C) F TI o $ elsi€ F {rJ .cI p\\ S€rsE# (U o< EeFr$ +. l( tr$F Ss EE; o l- os b€ n 5 E E aR \*i fr o o s > 8 p?g''E L l: cd13= .) cg {rf o.€ o = aR o ct) (d'= cE F q I c ;8 F q o lr Er I o \6' T' PP=G o 6S HEIIE o p -J< r o e ip F o -o ),I Ef,E';E ET$T $ egEETE iEEE$; PHYSICS UPDATE interconnectedness of seemingly different aspects to the one quoted above, Feynman says that if of natural behaviour, showing how just a few there are no charges inside the cavity there is principles can explain many things. These are no field inside; similarly (here is the context) truly classic works of educational insight. if there are no charges outside the cavity (that Recently, statements have been made, in the is, either if it is grounded or there are equal public domain, that accuse Feynman of making a but opposite charges inside, e.g., a dipole) there fundamental error in his discussion of electrostatic is no outside field in spite of the presence of shielding [2, 3]. Of particular interest is the charges inside. In the final sentence of the quoted following paragraph from volume II [1, ch. 5, p 9]: paragraph (which we omitted above because it was omitted in [2]) Feynman accurately concludes "We have shown that if a cavity is that, 'In electrostatics. the fields on the two completely enclosed by a conductor, sides of a closed conducting shell are completely no static distribution of charge outside independent.' This statement leaves little doubt as can ever produce any fields inside. to what is meant by'Shielding works both ways!'. This explains the principle of 'shielding' To further clarify the issue we note that when electrical equipment by placing it in a the enclosed charge q is at the centre of a metal can. The same argument can be spherical conducting shell, as considered in used to show that no static distribution [2], it is easy to confuse the external radial field with of charges inside a closed conductor can that due to the enclosed charge. The radial field, produce any fields outside. Shielding however, is actually produced by the charge q works both waysl" released on to the outer surface of the conducting Our purpose in this short article is to take a shell by the induced charge -q on its inner closer look at the issue of electrostatic shielding, surface. Thus the extemal field may be due to and Feynman's description of it, in order to correct the presence of an enclosed charge distribution the public record 12,31, in the physics education but it is not the field of (produced by) that communityt, on the validity of the discussion in enclosed charge distribution. Note the emphasis The Feynman Lectures on Physics. on the word 'inside' in Feynman's statement. The source of confusion stems from the fact To make this point clearer suppose that when that one usually thinks of electrostatic shielding the outside observer is asleep someone removes as the complete absence of an electric field. If the enclosed charge and places it on the outside a charged particle is placed near the outside surface. When the observer awakes he/she has ncr of an enclosed, hollow conductor no electric way to determine that there is now no enclosed field will be created inside the hollow interior. charge. The inside and outside of a conducting Whereas, if the charged particle is placed within enclosure are two disjoint regions, at least in the hollow interior an external electric field will electrostatics. be created. It is indeed true that the two cases This point becomes clear, as shown in figure differ in this way. With this normally understood 1(a). If the enclosed charge q is held off-centre interpretation of electrostatic shielding Feynman's the outer field is not directed radially outward statement is misleading. However, we suggest from the enclosed charge as would be required that, as discussed below, there is a more subtle by Coulomb's law if it were produced by that interpretation of 'Shielding works both waysl' that charge. Rather, it is directed radially outward reveals a more basic truth of Feynman's statement. from the centre of the shell. This is expected if the field is produced by the released charge 4 which gets uniformly distributed on the outer Exposition surface of the conducting sphere. The field inside the shell is the sum of the fields produced by the The paragraph quoted above (incompletely) must off-centre charge q and the unevenly distributec be placed its proper context relative to the in induced charge at the inner surface of the rest the discussion. the paragraph prior -q of In shell. The induced charge on the outer surface t ldeally, this short article should appear in the same journal is uniformly distributed while the induced charge as [2], but the editor did not agree with our views. on the inner surface is not. because this is the onlv 320 Phys. Educ.33(5) September 1998 + +++ + ++++ (a) (b) Figure 1. The shielding of an inner charge. ln (a) the field at a point P outside the conducting shell is joining (b) the outside field will Oi6cteo radially outwar*d trom the centre and not along the line +q,to P. ln density is large' be normal to the cube surlace and will be greater near-the cube corners where the charge way that the steady state field within the body of solid. It could be a closed wire screen. Shielding the conducting material can be made zero. The still occurs on both sides of the screen for distances induced charge -q on the inner surface of the sufficiently larger than the wire spacing. conductor distributes itself so as to completely cancel the field of the enclosed charge at distances remarks beyond the inner radius of the shell. Meanwhile, Concluding the charge q released on to the outer surface of Here we have shown that Feynman's statement the spherical shell distributes itself uniformly so about electrostatic shielding can be seen as correct that the field due to this charge is zero everywhere taken its full context. The fields within its outer radius. when in a closed conductor are As an additional illustration of the indepen- on the two sides of other because the conductor dence of the external field from the enclosed independent of each side from the charge distribution on charge distribution consider figure 1(b), where the shields one (note that Feynman says 'charge outer surface of the conducting material is non- the other side We sincerely hope spherical (cubic). The enclosed charge 4 is at distribution' in his statement). the centre of the spherical inner surface. Here that statements concerning errors of fundamental have the external field will be everywhere normal to physics inThe Feynman Lectures on Physics their the conducting surface instead of directed radially not discouraged educators from exposing outward from the charge at the centre. It will be students to this great work, for this would indeed stronger near the comers even though they are far- be a shame. ther from the centre. This field cannot be the field Richard Feynman was one of the few geniuses produced by the enclosed cbatge q which has a of this century. He has taught many of us that be- 1lr2 dependence. It must be the field produced ing an excellent physicist and an excellent physics by the induced charge 4 which distributes itself teacher are not mutually exclusive [4]. There has on the outer surface so as to produce both a zero been much written about his life. An enjoyable field within the body of the conductor and the nor- source of information about him can be found at mal external field mentioned above. http://www.eskimo.com/-billb/feynman.html. If the net enclosed charge is zero, for example if a dipole is placed within the hollow interior, there will be no external field at all. However, Acknowledgment in the absence of the conductor there will be a Ernest Behringer dipole field. In fact, any arbitrary distribution with The authors are grateful to Dr of the manuscript and equal amounts of opposite charges will result in no for reading an early version external electric field. The conductor need not be drawing figures 1(a) and 1(b)' Phys. Educ.33(5)September'1998 321 The beginning of Feynman's Nobel acceptance speech. About the electric field. lichard P. Feynman - Nobel Lecture http://nobelpri ze.orgl nobel_prizes/physics/laureates/ I 965/feyn. Nobelprize"0rs Richard P. Feynman Ihe Nobel Prize in Physics 1965 Nobel Lecture Nobel Lecture, December 11, 1965 The Development of the Space-Time View of Quantum Electrodynamics We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tccks, to not worry about the blind alleys or to describe how you had the wrong idea fjrst, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work, although, there has been in these days, some interest in this kind of thing.