Chapter 21 Magnetic Forces and Magnetic Fields 1
21.1 Magnetic Fields The phenomenon of magnetism (1) The magnetic compass In Class Demo The needle of a compass is a permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other. 2
21.1 Magnetic Fields (2) Iron/cobalt bar magnets The behavior of magnetic poles is similar to that of like and unlike electric charges. In Class Demo 3
21.1 Magnetic Fields Physics explanation The Earth is a very large magnet Its north magnetic pole (N) analogous to charge, near (but not exactly at) the geographical South Pole. Its south magnetic pole (S) analogous to charge,, near (but not exactly at) the geographical North Pole. Magnetic Field Lines come out of the north magnetic pole and go into the south magnetic pole in a manner that is analogous to electric field coming out of positive () charges and going into () charges. In the full electromagnetic theory by Maxwell (not in the scope of this course) there is a duality between electricity and magnetism. The magnetic field, B, like the electric field, is a vector field a vector valued function of position. 4
21.1 Magnetic Fields Surrounding a magnet there is a magnetic field. The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. In Class Demo (a) The magnetic field exerts a torque on magnets that tend to make them line up with the field (north pole pointing in the direction of the B field (b) The magnet, aligned with the field, will feel a force toward the region of stronger field (c) When anti-aligned with the field, the magnet will feel a force toward the region of weaker field http://www.youtube.com/watch?v=7lngrhvranw 5
21.1 Magnetic Fields The magnetic field lines and pattern of iron filings in the vicinity of a bar magnet and the magnetic field lines in the gap of a horseshoe magnet. Notice the similarity between the magnetic field lines around the bar magnet and the electric field lines around an electric dipole. They are in fact mathematically the same far away from the source. The bar magnet is a magnetic dipole: the same number of magnetic field lines come out of the north pole that go into the south pole. The magnetic monopole (like a magnetic charge), i.e. a pure N or S pole in a single object/particle, is not known to exist, but is not forbidden by Theory. 6
21.2 The Force That a Magnetic Field Exerts on a Charge When a charge is placed in an electric field, it experiences a force, called the Coulomb Force, according to F qe From Chapter 18 7
21.2 The Force That a Magnetic Field Exerts on a Charge When a charge is placed in a magnetic field, it experiences a force, called the Lorentz Force, according to: F B q( v B) The Lorentz force is nonvanishing if cross or vector product (a) The charge is no-zero, (b) The charge is moving, and (c) The velocity vector v of the charge has a non-zero component perpendicular to the magnetic field B The direction of v B is given by the Right Hand Rule (RHR) Or the Screw Rule The direction of F B is reversed from that of (v B ) for a negative charge q 8
21.2 The Force That a Magnetic Field Exerts on a Charge Right Hand Rule No. 1. Extend the right hand so the fingers point along the direction of the magnetic field and the thumb points along the velocity of the charge. The palm of the hand then faces in the direction of the magnetic force that acts on a positive charge. If the moving charge is negative, the direction of the force is opposite to that predicted by RHR-1 applied to v B v B Direction of magnetic force for positive charge The direction of v B is perpendicular to both v and B. The orientation is given by theright hand rule (RHR - 1shown here) v B v B sin in this instance, is between v and B. the angle (less than180) 9
21.2 The Force That a Magnetic Field Exerts on a Charge ( a) v B 0 when v B, (b) maximum when v B, (c) in between otherwise In Class Demo e http://www.youtube.com/watch?v=7yhwmwcxex8&feature=related By RHR-1: v B pointsup These are electrons so the force pointsdown 10
21.2 The Force That a Magnetic Field Exerts on a Charge DEFINITION OF THE MAGNETIC FIELD The magnitude of the magnetic field at any point in space is defined as: B q o F vsin where the angle (0<θ<180 o ) is the angle between the velocity of the charge and the direction of the magnetic field. SI Unit of Magnetic Field: newton second coulomb meter 1tesla T 1gauss 10 4 tesla Magnetic field at thesurface of the Earth ~ 0.5 gauss 11