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PHYS 222 Worksheet 14 – Magnetic Field Supplemental Instruction Iowa State University Leader: Course: Instructor: Date: Alek Jerauld PHYS 222 Dr. Paula Herrera-Siklódy 2/21/12 Useful Equations F qv B F q vB sin( ) F q(E v B) Magnetic force on a moving charged particle Magnitude of the magnetic force. ∅ is the angle between the velocity vector and the B-field vector Total force exerted on a moving charged particle due to electric and magnetic fields. Magnetic field unit: Tesla [T] = 1 N/Am or Gauss [G] = 10-4 T Magnetic Interactions A moving charge or a current creates a magnetic field in the surrounding space The magnetic field exerts a force F on any other moving charge of current that is present in the field Diagrams Right hand rule for magnetic force: Related Problems 1) A particle with a charge of −1.20×10−8 C is moving with instantaneous velocity v = (4.60 m/s) i + (-3.40 m/s) j. What is the force exerted by a magnetic field B = (1.40 T) i ? (Book 27.1) Hint: F qv B 0 4.60 1.40 Fx F 1.2(108 ) 3.40 0 Fy 0 0 0 Fz 6.53(108 ) N 2) An electron moves at 2.60×106 m/s through a region in which there is a magnetic field of unspecified direction and magnitude 7.60×10−2 T. What is the largest possible magnitude of the acceleration of the electron due to the magnetic field? What is the smallest possible acceleration? (Book 27.6) When magnetic field is perpendicular to the velocity, acceleration is maximum: F ma F qvB sin( ) ma qvB sin(90 ) qvB a (1) 3.48(1016 ) m / s 2 m When magnetic field is parallel to the velocity, acceleration is minimal: ma qvB sin(0 ) a qvB (0) 0 m / s 2 m 3) In an experiment with cosmic rays, a vertical beam of particles that have charge of magnitude 3e and mass 12 times the proton mass enters a uniform horizontal magnetic field of 0.250 T and is bent in a semicircle of diameter 95.0 cm. What is the speed of the particles? (27.22) acentripetal v2 d /2 v2 m 3qvB sin(90 ) d /2 3qdB(1) v 2.84(106 ) m / s (2)3me 4) A singly charged ion of 7Li (an isotope of lithium) has a mass of 1.16×10−26 kg. It is accelerated through a potential difference of 260 V and then enters a magnetic field with magnitude 0.726 T perpendicular to the path of the ion. What is the radius of the ion’s path in the magnetic field? (Book 27.26) First find the initial speed of the particle before entering the magnetic field: W KE 1 1 1 mv12 mv0 2 , v0 0 W mv12 2 2 2 W qV 1 mv12 qV 2 2qV v12 m Now use centripetal acceleration equation and force equation to solve for R: 2qV m 2 v 2qV ac 1 R mR mac qvB sin(90) v12 m 2qV 2qV 1 2mV q BR 8.46(103 ) m mR m B qe 5) If two deuterium nuclei (charge +e, mass 3.34 x 10-27kg) get close enough together, the attraction of the strong nuclear force will fuse them to make an isotope of helium, releasing vast amounts of energy. The range of this force is about 10-15 m. This is the principle behind the fusion reactor. The deuterium nuclei are moving much too fast to be contained by physical walls, so they are confined magnetically. (a) How fast would two nuclei have to move so that in a head-on collision they would get close enough to fuse? (Treat the nuclei as point charges, and assume that a separation of 10-15 m is required for fusion.) kq 2 kq 2 F ma 2 a x mx 2 d da kq 2 v 2 dx dx mx kqe 2 kq 2 v v0 , v 0 v0 8.3(106 ) m/ s md md (b) What strength magnetic field is needed to make deuterium nuclei with this speed travel in a circle of diameter 2.60 m? For a circular motion, acceleration is only present in the centripetal direction: v0 2 F ma, a d /2 F qv0 B sin(90) mv0 2 qv0 B sin(90) d /2 mv0 B 0.13 T qd / 2