Can someone explain why the addition of the small fixed magn

Can someone explain why the addition of the small fixed magnetic field to the external alternating magnetic field changed the position and signal height of the absorption peaks. Hint: Combine the vectors of the various magnetic fields to explain the overall effect. this deals with a small magnet and a helmholtz coils

Solution

I have to given answer with expermental procedure,but not given to the diagram.

The external magnetic field, Bo , is provided by the Helmholtz coils. These coils produce a very uniform magnetic field in the area between the coils which is oriented perpendicularly to the cross sectional area of the coils. The molecular material with one unpaired electron outside a closed subshell is a red crystalline powder called DPPH (diphenylpicrylhydrazyl). The sample of DPPH is inserted inside a simple helical coil which is located at the tip of the aluminum probe. The coil and sample are used as the inductive portion of an LC \"tank circuit\". The tank circuit has a resonant frequency R = (1 / (2 LC))1/2.

The current oscillations in the tank circuit will produce a small amplitude (of radio frequency in our case) electromagnetic field inside the coil wrapped around the sample. If the feedback resistor R is adjusted so that the oscillator is barely oscillating (the net gain in the circuit exceeds the net loss by a very small amount), then the amplitude of oscillation will be very sensitive to any changes in absorption of radio frequency energy in the circuit. In particular, the absorption of energy due to electron spin resonance in the sample will give a large change in the amplitude of oscillation. Such a circuit is called a marginal oscillator. The amplitude of the oscillations is displayed on channel A of the oscilloscope. The capacitor C is variable, which allows us to change R . The frequency of oscillation of the oscillator is measured by the frequency counter. The sample and coil are oriented so that the magnetic field , Brf , of the electromagnetic waves in the rf field is parallel to the long axis of the sample coil which in turn is parallel to the long axis of the probe. The rf coil and sample are placed between the Helmholtz coils such that Brf is perpendicular to Bo . In general then, one chooses the frequency R by adjusting C . One adjusts R so that the oscillator is barely oscillating. Bo is varied linearly at a rate of 60 Hz, and whenever Bo is such that hR = 2 µs Bo there is a decrease in the amplitude of the radio frequency oscillation, as displayed on the oscilloscope, which represents electron spin resonance. Bo can be computed from the voltage displayed on channel B of the scope and R can be read from the frequency counter.

Turn on the oscilloscope and the Daedal on ESR power supply. Press the SETUP button on the scope. A menu will appear at the bottom of the scope display. Press the left most button under the scope display screen until the number 1 is displayed in the left most part of the menu display. Press the third button from the left to recall the scope setup stored in memory location 1. This should set all of the controls on the scope to values that will give you a good display of the data being fed into the scope from the ESR equipment. The display on the oscilloscope will be either a noisy horizontal line or a line with two or four absorption peaks in it. If the display is the former, then adjust the feedback resistor until the two or four peaks are displayed. If you adjust the feedback resistor throughout its entire range and cannot obtain the four peaks, then there is a problem with either the marginal oscillator or the probe. As the current in the Helmholtz coils increases from zero, the magnetic field strength increases proportionally and the energy level of the unpaired electron outside a closed sub shell splits into two levels with the amount of separation proportional to the strength of the field. The trace starts tracking horizontally to the right (or left) reflecting this increase in the magnetic field strength. There is no vertical deflection of the trace since, initially, the energy level separation, 2µoBo , is less than the energy of the photons in the rf field. Under those conditions, little or no energy absorption can take place. When the magnetic field strength reaches a value such that energy level separation exactly equals the photon energy (h = 2µoBo), the electrons in the DPPH absorb energy from the rf field and the vertical deflection of the trace becomes large. As the magnetic field continues to grow larger, the energy level separation becomes greater than the energy of the photons in the rf field and absorption stops. The signal amplitude returns to its no absorption level. The trace to this point then would be a flat horizontal section followed by an absorption peak followed by another horizontal flat section. As the magnetic field strength reaches its maximum and decreases toward zero, the trace should retrace itself. When h = 2µoBo an absorption peak should again occur. It should, however, occur in the same horizontal position as it did when the magnetic field strength was increasing. The pattern should then repeat itself on the other side of the zero field position resulting in just two peaks. The reason that you see four peaks is because the electronic circuitry used to monitor the system introduces a phase shift in the signal coming from the 0.1 ohm resistor and from the rf amplitude output on the oscillator. The function of the phase shifter is to eliminate this phase shift and thereby make the Bo measurements easier.

As noted in the introduction, the electron transitions are induced only by perpendicular oscillating magnetic fields. Since only the component of the field Brf of the sample coil perpendicular to the external field is effective in causing transitions, the observed signal height should be proportional to sin2 where is the angle between the axis of the oscillator coil (the probe) and the direction of the external magnetic field Bo. Observe the effect on the positions and signal heights of the absorption peaks when a small fixed magnetic field is superimposed on the alternating external magnetic field Bo . This may be done by bringing up a small permanent magnet.