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www.GOALias.blogspot.comMagnetism andMatter(b) If field lines were entirely confined between two ends of a straightsolenoid, the flux through the cross-section at each end would benon-zero. But the flux of field B through any closed surface mustalways be zero. For a toroid, this difficulty is absent because ithas no ‘ends’.(c) Gauss’s law of magnetism states that the flux of B through anyclosed surface is always zero Ñ ∫ Bgd s = 0 .SIf monopoles existed, the right hand side would be equal to themonopole (magnetic charge) q menclosed by S. [Analogous toGauss’s law of electrostatics, ∫ Bgd s = µS0qwhere q mis them(monopole) magnetic charge enclosed by S.](d) No. There is no force or torque on an element due to the fieldproduced by that element itself. But there is a force (or torque) onan element of the same wire. (For the special case of a straightwire, this force is zero.)(e) Yes. The average of the charge in the system may be zero. Yet, themean of the magnetic moments due to various current loops maynot be zero. We will come across such examples in connectionwith paramagnetic material where atoms have net dipole momentthrough their net charge is zero.EXAMPLE 5.75.4 THE EARTH’S MAGNETISMEarlier we have referred to the magnetic field of the earth. The strength ofthe earth’s magnetic field varies from place to place on the earth’s surface;its value being of the order of 10 –5 T.What causes the earth to have a magnetic field is not clear. Originallythe magnetic field was thought of as arising from a giant bar magnetplaced approximately along the axis of rotation of the earth and deep inthe interior. However, this simplistic picture is certainly not correct. Themagnetic field is now thought to arise due to electrical currents producedby convective motion of metallic fluids (consisting mostly of molteniron and nickel) in the outer core of the earth. This is known as thedynamo effect.The magnetic field lines of the earth resemble that of a (hypothetical)magnetic dipole located at the centre of the earth. The axis of the dipoledoes not coincide with the axis of rotation of the earth but is presentlytitled by approximately 11.3º with respect to the later. In this way of lookingat it, the magnetic poles are located where the magnetic field lines due tothe dipole enter or leave the earth. The location of the north magnetic poleis at a latitude of 79.74º N and a longitude of 71.8º W, a place somewherein north Canada. The magnetic south pole is at 79.74º S, 108.22º E in theAntarctica.The pole near the geographic north pole of the earth is called the northmagnetic pole. Likewise, the pole near the geographic south pole is calledGeomagnetic field frequently asked questionshttp://www.ngdc.noaa.gov/seg/geomag/185