8.02Experiment 6: Forces and Torques on Magnetic Dipoles1. To observe and measure the forces and torques acting on a magnetic dipole placed in an external magnetic field.REMARK: We will only measure the torque on the dipole, (parts 1-3 below). If you have the time you may want to try and observe the forces on the dipole in parts 4-5 but it is not required.INTRODUCTIONGENERALIZED PROCEDUREThis lab consists of five main parts. In each you will observe the effects (torque & force) of different magnetic field configurations on the disk magnet (a dipole).Part 2: Reversing the fieldYou will reverse the direction of the field and see what happens.Here you slowly pull the disk magnet up from the bottom of the Helmholtz apparatus (in Helmholtz mode) and out through the top, observing any torques or forces on the magnet.Here you repeat part 1 in anti-Helmholtz configurationHere you slowly pull the disk magnet up from the bottom of the Helmholtz apparatus (in anti-Helmholtz mode) and out through the top, observing any torques or forces on the magnet.END OF PRE-LAB READINGEXPERIMENTAL SETUPMEASUREMENTSPart 1: Dipole in Helmholtz ModePart 2: Reversing the LeadsPart 3: Moving a Dipole Along the Axis of the Helmholtz ApparatusPart 4: Dipole in Anti-HelmholtzPart 5: Moving a Dipole Along the Axis of an Anti-Helmholtz CoilMASSACHUSETTS INSTITUTE OF TECHNOLOGYDepartment of Physics8.02Experiment 6: Forces and Torques on Magnetic DipolesOBJECTIVES 1. To observe and measure the forces and torques acting on a magnetic dipoleplaced in an external magnetic field.REMARK: We will only measure the torque on the dipole, (parts 1-3 below). If youhave the time you may want to try and observe the forces on the dipole in parts 4-5but it is not required.PRE-LAB READINGINTRODUCTIONIn this lab you will suspend a magnetic dipole (a small but strong bar magnet) in the fieldof a Helmholtz coil (the same apparatus you used in Expt. 5). You will observe the forceand torque on the dipole as a function of position, and hence external field. The Details: Magnetic Dipoles in External FieldsAs we have discussed in class, magnetic dipoles are characterized by their dipole moment, a vector that points in the direction of the B field generated by the dipole (at the centerof the dipole). When placed in an external magnetic field B, they have a potential energy -DipoleU = ⋅ì BrrThat is, they are at their lowest energy (“happiest”) when aligned with a large external fieldTorqueWhen in a non-zero external field the dipole will want to rotate to align with it. Themagnitude of the torque which leads to this rotation is easily calculated:( ) ( )cos sindU dB Bd dτ μ θ μ θθ θ= = − = = ×ì BrrAgain, the direction of the torque is such that the dipole moment rotates to align with thefield (perpendicular to the plane in which and B lie, and obeying the right hand rulethat if your thumb points in the direction of the torque, your fingers rotate from to B.E04-1ForceIn order to feel a force, the potential energy of the dipole must change with a change in itsposition. If the magnetic field B is constant, then this will not happen, and hence thedipole feels no force in a uniform field. However, if the field is non-uniform, such as iscreated by another dipole, then there can be a force. In general, the force is quitecomplex, but for a couple of special cases it is simple:1) If the dipole is aligned with the external field it seeks higher field2) If the dipole is anti-aligned it seeks lower fieldThese rules can be easily remembered just by remembering that the dipole always wantsto reduce its potential energy. They can also be remembered by thinking about the waythat the poles of bar magnets interact – opposites attract while likes repel.In one dimension, when the dipole is aligned with the field, a rather straight forwardmathematical expression may also be derived:dU d dBF Bdz dz dzμ μ=− = =Here it is important to note that the magnitude of the force depends not on the field but onthe derivative of the field. Aligned dipoles climb uphill. The steeper the hill, the moreforce they feel.APPARATUS1. Teach Spin ApparatusE04-2Figure 1 The Teach Spin Apparatus (a) The Helmholtz apparatus has a tower assembly(b) placed along its central axis. The tower contains a disk magnet which is free to rotate(on a gimbal) about an axis perpendicular to the tube and constrained to move vertically.The amount of motion can be converted into a force knowing the spring constant of thespring.The central piece of equipment used in this lab is the Teach Spin apparatus (Fig. 1). Itconsists of the Helmholtz coil that you used in experiment 5, along with a Plexiglas tubecontaining a magnet on a spring. The magnet can both rotate and move vertically,allowing you to visualize both torques and the forces on dipoles.It will be useful to recall some results from experiment 5 involving the Helmholtz coil. There are three different modes of operation – you can energize just a single coil, both coils in parallel (Helmholtz configuration) or both coils anti-parallel (anti-Helmholtz). The field profiles (as well as the derivatives of those profiles – necessary for thinking about force) look like the following:E04-3(a) (b)-2 -1 0 1 20Anti-HelmholtzSingle CoilHelmholtzTop CoilBottom CoilDistance along the central axis (z/R)-2 -1 0 1 20Anti-HelmholtzSingle CoilHelmholtzTop CoilBottom CoilDistance along the central axis (z/R)Figure 2: The z-component of the magnetic field and its derivative for the three modesof operation of the Helmholtz coil. See page the last page of this write-up for an “iron-filings” representation of these three field configurations.2. Power SupplyWe will also use the same power supply as in experiment 4 in order to create large enough fields in the Helmholtz apparatus to exert a measurable force on the magnet.E04-4GENERALIZED PROCEDUREThis lab consists of five main parts. In each you will observe the effects (torque & force)of different magnetic field configurations on the disk magnet (a dipole).Part 1: Dipole at center of Helmholtz CoilYou will move the disk magnet to the center of the Helmholtz apparatus and randomlyalign it and then see what happens when the coil is energized.Part 2: Reversing the fieldYou will reverse the direction of the field and see what happens.Part 3: Moving Through the Helmholtz ApparatusHere you slowly pull the disk magnet
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