Semester PHYS1002 2 2004 Tutorial 4
PHYS1002 2004 Tutorial Sheet No 4
Due: 27/8/04
Make sure that you ask questions during the oral tests. The tutor will not take them into account when marking the student at the board, but you will get credit for participation.
Study Guide
The magnetic force acts only on moving charges that have a component of velocity perpendicular to the field. A charge at rest or moving along the field direction experiences no force. In a uniform magnetic field a net torque, but no net force, is exerted on either a permanent dipole or a current loop. The magnetic force on a moving particle is directed perpendicularly to both the field direction and the direction of the velocity of the charge. Therefore, no work is ever done by magnetic forces. You can find the directions of the magnetic forces that two moving charges exert on each other, as follows. First, at the location of one charge, find the direction of the magnetic field due the other charge; and repeat the process at the location of the other charge. Second, find the directions of the forces exerted by these magnetic fields. Use the same two steps to find the direction of the forces exerted by two current elements on each other. Try to visualize the three dimensional aspects of magnetism. Draw yourself pictures from different perspectives to understand the problem better. Extra problems: 1. A particle of charge q and mass M moves in a circle of radius r and with angular velocity . a) Show that the average current is I = q /2 and that the magnetic moment has the magnitude m=0.5q 2. b) Show that the angular momentum of this particle has the magnitude L=Mr2 and that the magnetic moment and angular momentum vectors are related by m=(q/2M)L. 2. (Hard) A wire bent in some arbitrary shape carries a current i in a uniform magnetic field B. Show that the total force on the part of the wire from some point a to some point b is F=i x B where is the vector from a to b.
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PHYS1002 Semester 2 2004 Tutorial 4
Problems
1) Hall voltage and Motion of charges in magnetic fields
a) Because blood contains charged ions, moving blood develops a Hall voltage across the diameter of an artery. The blood in a large artery with a diameter of 0.85 cm has a flow speed of 0.6 m/s. If a section of this artery is in a magnetic field of 1.2 T, what is the potential difference across the diameter of the artery? b) A cyclotron for accelerating protons has a magnetic field of 1.6 T and a radius of 1.2 m. i) What is the cyclotron frequency? ii) Find the maximum energy of the protons when they emerge. iii) How will your answers change if deuterons, which have the same charge but twice the mass, are used instead of protons?
2) Magnetic field due to moving charges
A charge of 3 10 6 C is distributed uniformly around the rim of a cardboard disk of radius 10 cm, and this disk is made to spin about its axis at the rate of 24 revolutions per second. a) What is the current generated by the motion of the charge? b) What is the magnetic field that this current produces at the center of the disk?
3) Magnetic moment and torque
A horizontal circular loop of wire of radius 25 cm carries a current of 20A. At the location of the loop, the magnetic field of the Earth has a magnitude of 0.45 10 4 T and points down at an angle of 15 o with the vertical. Find the magnetic moment of this loop and hence the magnitude of the torque that Earths magnetic field exerts on it.
4) Magnetic field due to a ring
A ring of radius 7.5 cm is placed concentrically around a ring of radius 5 cm. Each ring carries a current of 5A. B
6cm 8cm a) What is the magnitude of the magnetic field at the centre of the rings if two currents flow in the same direction? b) If they flow in opposite directions?
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PHYS1002 2 Semester 2004 Tutorial 4
5) Amperes Law
The electric cable supplying DC to an electric clothes dryer consists of two long straight wires separated by a distance of 1.5cm. Opposite currents of 25 A flow on these wires. What is the magnetic force experienced by a 1 cm segment of wire due to the entire length of the other wire?
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PHYS1002 Semester 2 2004 Tutorial 4
Mad Physicists
The Shanghai Maglev
Article by: Lawrence Tse First published: 31 Dec 2002 Latest update: 01 Jan 2004
Futuristic Train in Operation
The first official test run of the worlds first commercial magnetic levitation [maglev] train service took place on 31st December 2002 in Shanghai, China. Chinese Premier Zhu Rongji and German Chancellor Gerhard Schrder were among the first few passengers on the maiden voyage. The train service is planned to be available to the public from September 2003 onwards. This Sino-German joint project involves the construction of an elevated, doubletrack guideway from the Pudong Interational Airport to the Long Yang Road subway station near the Lujiazui Financial District in Pudong. The maglev trains are supplied by Transrapid International, a joint company established by Siemens and ThyssenKrupp. With a maximum speed of 430km/h, the 30km journey takes only 8 minutes! The same journey takes at least 45 minutes for a bus or a taxi.
A Brief History of the Shanghai Maglev Project
Magnetic levitation [maglev] is an innovative technology and is now applied in high-speed trains. Although the Germans and the Japanese have been Shanghai Maglev Train at Long Yang Station doing solid research on magnetic levitation trains since the 1970s and numerous test vehicle trials have been carried out, commercial maglev systems were not realised until the city of Shanghai and Transrapid International [Germany] signed a contract to build a short airport railway link in January 2001. Construction of the 30km elevated track started in March 2001. The first section of maglev train left the ThyssenKrupp plant in Kassel [Germany] in June 2002 and arrived in Shanghai early August 2002. Since the arrival of the train, German maglev experts were invited to ensure the smooth running of tests, for testing safety and reliable of trai...