2017 USA Physics Olympiad Exam Part A 10 Solution Note that the two iron balls create a magnetic field near the compass that behaves like that of the ship as a whole.There is a component directed toward the bow given by Bo =-2Be sin o cos0 and a component directed toward the starboard given by Bs 2Br cos oo sin where the factors of 2 are because there are two balls.Note that 0 is the ship heading while o is the angle between North and the location of the compass relative to one of the balls.Thus, if the field is corrected for the maximum angles it will necessarily cancel out the induced ship field for all of the angles,so that 60=0 for all 0.Effectively,this means placing the balls to make Ko=K's. Copyright C2017 American Association of Physics Teachers2017 USA Physics Olympiad Exam Part A 10 Solution Note that the two iron balls create a magnetic field near the compass that behaves like that of the ship as a whole. There is a component directed toward the bow given by Bb = −2Bθ ∝ sin φ ∝ cos θ and a component directed toward the starboard given by Bs = 2Br ∝ cos φ ∝ sin θ where the factors of 2 are because there are two balls. Note that θ is the ship heading while φ is the angle between North and the location of the compass relative to one of the balls. Thus, if the field is corrected for the maximum angles it will necessarily cancel out the induced ship field for all of the angles, so that δθ = 0 for all θ. Effectively, this means placing the balls to make Kb = Ks. Copyright c 2017 American Association of Physics Teachers