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Unformatted text preview: 26 MAGNETIC FIELDS AND THE MAGNETIC DIPOLE OBJECT To get the magnetic dipole two ways: plot the magnetic field vs. 1/r 3 and to plot the frequency squared (w^2) in a magnetic field vs. that magnetic field. ( It is extremely important to use SI units in this lab. Use meters, amperes and Tesla as your units of distance, current and magnetic field .) APPARATUS Ring magnet; helmholtz coil, power supply, string, ruler, magnetic field sensor, datastudio software, interface box, rod on tripod, cross connector, cross rod from photogate platform THEORY The magnetic field of a ring magnet is similar to that produced by a pair of unlike electrical point charges (an electric dipole); however, no such thing as a “magnetic charge” exists in nature. Instead, magnetic fields may be described only in terms of a dipole. It is as if “magnetic charges” (or poles) exist only in pairs. It may be shown mathematically that the magnetic field produced by a dipole at any point along a line intersecting the dipole, and measured parallel to it is given exactly by: ( ) 2 3 2 2 2 ) ( z R z B z + = μ π μ , where 2 2 1 R R R + = Eq. 1) Figure 1) The magnetic field of a circular magnet is shown. The dipole moment and the magnetic field on the z axis are indicated. The inner and outer radii of the ring magnet are R 1 and R 2 . μ B z 27 The dipole moment also determines the movement of the magnet in an applied field. The torque on a dipole in a magnetic field is α μ τ I B e − = × = v v v , E q . 2 ) where I is the moment of inertia, B e is the external field and α is the angular acceleration. This becomes the approximate differential equation for small angles of deflection,...
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- Fall '09
- Magnetic Field