NMR model

What it shows:  Using the classical description of the motion of a spin in an external magnetic field, the demonstration helps visualize NMR in the time domain. The nuclear magnet and its classical vector model are represented by a spinning ball with magnets attached. A rotating mass is characterized by its angular momentum L, which is the analog of the magnetic moment mu, which characterizes a rotating charge distribution. The spinning ball mimics protons in that it has both angular momentum as well as an "intrinsic" magnetic moment. The torque provided by gravity causes the ball to precess, gravity being the proxy for the static magnetic field in an actual NMR apparatus.  Finally, a pair of Helmholtz coils provide the AC magnetic field (RF field in real NMR). One can secure a "spin up" or "down" state when the AC field is applied at the appropriate frequency and phase (the Larmor frequency analog).

How it works:  The drawing schematically depicts the arrangement of the the most basic elements of an NMR apparatus. The test tube contains a substance whose atoms or molecules are rich in protons.

NMR is possible because nuclei of many atoms possess magnetic moments and angular momenta. A magnetic moment interacts with a static magnetic field in such a way that the field tries to force the moment to line up along it, just like a compass needle lines up with the earth's field. The significance of the angular momentum, which is proportional to the moment, is that it makes the nuclei precess around the magnetic field when it experiences the torque due to the field acting on the moment. The result is that the nuclei precess about the field rather than oscillating in a plane like a compass needle. This precession is exactly analogous to a top, with its angular momentum along its spinning axis, precessing about the earth's gravitational field. Instead of a top, we use an air-supported gyro ball. Magnets attached to its spinning axis provide the magnetic moment. The torque is due to the gravitational field. Given a spin, the gyro ball precesses in the direction shown.

The precessing gyro ball (with its magnetic moment) is positioned in the center of a large set of Helmholtz coils as depicted in the next drawing.

The magnetic field of these coils can be made to alternate in direction by manually reversing the current with a switch. With a little practice, it is relatively easy to synchronize the switching of the field with the precession period, since it is of the order of seconds. (This is the analog of matching the RF frequency with the Larmor precession.) In doing so, one can secure a spin up or down state. For example, suppose the magnetic field direction is toward the back of the coils at the time the spinning magnetic dipole is in the position shown (the angular momentum vector is pointing roughly in the one o'clock direction). The magnetic moment will experience a torque towards the back of the coils, which in turn tends to try to change the direction of the angular momentum vector towards the side (towards 9 o'clock). The result is that the magnetic dipole moves upward. If you get confused, just remember the rule of thumb:  when a force (torque) is applied to a spinning gyro, it always responds by moving in a direction that is perpendicular to the applied force. Reverse the current when the dipole is in the opposite direction. By repeatedly switching the magnetic field in this manner, you can make the angular momentum vector (and the magnetic dipole) vertical. That will be "spin up." Spin down may be secured by switching in the opposite direction.

Setting it up:  Set up the Helmholtz coils and power supply on one of the large blue carts. The Sorensen SRL 20 - 25 is the preferred power supply for this application. Observe the color coded polarities when connecting it to the Helmholtz coils. When properly connected, the positive current will pass CW through the coils (as viewed from the front) and the magnetic field direction will be toward the back. Position the air-support for the gyro ball inside the coils. Use the air compressor with ballast tank.

Comments:  This demonstration is rich in content and brings together many physics concepts that the students have encountered during the course:  torques, angular momentum, as well as electromagnetic phenomena. It's rather satisfying to put them all together to visualize NMR.