The induced magnetic field must therefore have field lines that go down on the inside of the loop. The current direction indicated by the arrows on the circuit loop will achieve this. Test this by using the Right Hand Rule. Put your right thumb in the direction of one of the arrows and notice what the field curls downwards into the area enclosed by the loop.
In the second diagram the south pole is moving away. This means that the field from the magnet will be getting weaker. The response from the induced current will be to set up a magnetic field that adds to the existing one from the magnetic to resist it decreasing in strength.
Another way to think of the same feature is just using poles. To resist an approaching south pole the current that is induced creates a field that looks like another south pole on the side of the approaching south pole. Like poles repel, you can think of the current setting up a south pole to repel the approaching south pole.
In the second panel, the current sets up a north pole to attract the south pole to stop it moving away.
We can also use the variation of the Right Hand Rule, putting your fingers in the direction of the current to get your thumb to point in the direction of the field lines or the north pole. We can test all of these on the cases of a north pole moving closer or further away from the circuit. For the first case of the north pole approaching, the current will resist the change by setting up a field in the opposite direction to the field from the magnet that is getting stronger.
Use the Right Hand Rule to confirm that the arrows create a field with field lines that curl upwards in the enclosed area cancelling out those curling downwards from the north pole of the magnet. Like poles repel, alternatively test that putting the fingers of your right hand in the direction of the current leaves your thumb pointing upwards indicating a north pole.
The approach for looking at the direction of current in a solenoid is the same the approach described above. The only difference being that in a solenoid there are a number of loops of wire so the magnitude of the induced emf will be different. The flux would be calculated using the surface area of the solenoid multiplied by the number of loops. Remember: the directions of currents and associated magnetic fields can all be found using only the Right Hand Rule. When the fingers of the right hand are pointed in the direction of the magnetic field, the thumb points in the direction of the current.
When the thumb is pointed in the direction of the magnetic field, the fingers point in the direction of the current. The direction of the current will be such as to oppose the change. We would use a setup as in this sketch to do the test:. In the case where a north pole is brought towards the solenoid the current will flow so that a north pole is established at the end of the solenoid closest to the approaching magnet to repel it verify using the Right Hand Rule :.
In the case where a north pole is moving away from the solenoid the current will flow so that a south pole is established at the end of the solenoid closest to the receding magnet to attract it:. In the case where a south pole is moving away from the solenoid the current will flow so that a north pole is established at the end of the solenoid closest to the receding magnet to attract it:. In the case where a south pole is brought towards the solenoid the current will flow so that a south pole is established at the end of the solenoid closest to the approaching magnet to repel it:.
An easy way to create a magnetic field of changing intensity is to move a permanent magnet next to a wire or coil of wire. The induced current generates a magnetic field.
The induced magnetic field is in a direction that tends to cancel out the change in the magnetic field in the loop of wire. So, you can use the Right Hand Rule to find the direction of the induced current by remembering that the induced magnetic field is opposite in direction to the change in the magnetic field. Electromagnetic induction is put into practical use in the construction of electrical generators which use mechanical power to move a magnetic field past coils of wire to generate voltage.
However, this is by no means the only practical use for this principle. If we recall, the magnetic field produced by a current-carrying wire is always perpendicular to the wire, and that the flux intensity of this magnetic field varies with the amount of current which passes through it. Here we are interested to learn about FRF initially in the range 0. We studied both methods and found that each had drawbacks: the HPF resulted in phase shifts and temporal distortion of the time series, while preserving the desired frequency range and avoiding spurious presentation of frequencies below the cutoff.
Polynomial detrending preserved the time relationship of peaks in the time series no phase shifts but had variable and somewhat unpredictable effects on the power spectrum. The phase shifts from filtering do not degrade the power spectral analysis. The observed FR fluctuations are not attributed significantly to ionospheric variations. Various ionospheric disturbances on time scales of minutes to hours may have associated RM of on the order of 0.
A power law relation appears over frequency range approximately 0. The spectral flattening below 0. Due to these upper and lower frequency bounds on the power law region, as well as the localized enhancements of spectral power around 1.
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For the lower end of the power law fit, the 0. The spectral index was calculated by linear regression on the double log plot, using only the upper and lower regions above for the fitting. These issues are addressed in the next section. Also, the simulations were used to address the expected outcomes from processing of shorter data segments, e. These shorter analysis segments were of interest to examine temporal changes in spectral index and FRF RMS values across the full data record. A system of oscillators was generated computationally, with frequencies distributed evenly over 0. A histogram of the resulting simulation fluctuations showed reasonably Gaussian distribution of fluctuations.
The final amplitude scaling was applied to force the simulation RMS amplitude to 0. The spectrum from our observations is coplotted in blue. The spectral peaks at 3. A crescendo FRF transient is observed in the first quarter of the record, while the remainder of the time series suggests more stationary processes. The finding of peaks at 3. Changes in spectral structure were therefore investigated by interval analysis to explore radial dependencies and to search for more homogenous snapshots of coronal activity.
A sliding window algorithm was applied to the observed FRF time series as well as the simulated time series. For the observations, frame advance corresponds to increasing solar offset. FRF power within each frequency range v 1 to v 2 was obtained from the power spectral density G v by integrating over the specific frequency band 3.
In contrast, the 1. When the power law spectral index was determined over range of 0.
We concluded that the 1. Three main points emerge from the sliding frame analysis. Second, in 1. The FRF amplitudes increase near the end of the frame. Spectral peaks at 3. The three spectra were similar and generally confined within the 3 standard deviation envelope. We found overall concordance with previous coronal sounding FR studies that had been conducted with longer radio wavelengths, greater solar offsets, and different recording equipment.
Initial comparisons are now presented. We found it useful to separate the data analysis frame with the transient event from those showing only the general background fluctuation spectrum. Efimov et al. Lesser transient surges are seen thereafter. Here we computed the electron concentration using the radio data of Mercier and Chambe [ ].
It was felt that electron concentration data specific to our observation time frame would be more appropriate than use of a general parameter formula. A uniform pattern of magnetic fluctuations should result in FRF that scale down with increasing solar offset due to decreasing electron concentration; see equation 8 below. Bidirectional wave transmission is important in MHD wave energy dissipation. The present study supports the concept of a field of randomized fluctuations on the background magnetic field.
When we ran the simulated oscillator system, a number of features of such a field were reproduced. Hollweg et al. Other studies [ Andreev et al. The role these waves may play in solar wind acceleration is still being evaluated by the solar physics community [see Roberts , ]. These questions can be explored by studying combined data sets that cover a wider range of solar offsets, solar latitudes, and phases in the solar cycle. The 3. Mathioudakis et al. As discussed in section 3. These randomized waves are expected to be uncorrelated and therefore may be summed along a given LOS as a random walk.
Finally, we assume that most FRFs originate near the proximate point where the plasma density is greatest.
The effect of bulk plasma flow on the wave energy flux will be adressed below following equation The correlation length may be approached in a number of ways. Some consider the correlation scale as roughly equal to the spacing between magnetic flux tubes [ Hollweg et al. Others [ Spangler , , Andreev et al. Here we use the interpretation given in Hollweg et al.
Many such waves should be crossing the LOS at any given time, but only those fairly near the proximate point will be passing through a high enough electron concentration to affect the FR appreciably. Review of density and radial magnetic field profiles at solar offset 1. We therefore take 0. Different approaches are available to estimate the local magnetic field strength B.