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A solenoid is a long straight coil of a wire bent into a circle to produce electromagnetic effects. When the right-hand grip rule is applied is applied to the single coil of the solenoid, the electric field lines will align themselves along with the current in the wire. In figure 3 below, there is a representation of the edge of view a single solenoid coil whereby the electric current enters the page on top and leaves the page at the bottom. From the figure, it is clear that field lines inside the coil points mostly to the left, a point that is also known as solenoid axis. On the other hand, on the outer side of the coil, they mostly point towards the right (Giancoli, 2008).
When the electric fields for the several closest coils of an ideal solenoid are superimposed, the elements of the fields inside the coil that are not aligned towards the left cancel out each other leaving only the fields pointing to the left as shown in figure 4. Additionally, the similar field cancellation also occurs on the outer side of the solenoid and the electric fields are aligned towards the right. As a result of field cancellations on the outer and inner sides of the solenoid, the electric field concentration often becomes significantly weaker outside the coil than on the interior side. Therefore, longer coils often create weaker electric fields on the outer side (Giancoli, 2008). On the other hand, when the coil is infinitely long, there will be zero fields on the outer side (Ibid).
Figure 3(Giancoli, 2008)
Figure 4(Giancoli, 2008)
To determine the magnitude and value of the field, the application of Ampere's law is essential. According to Amperes law, the line integral of the magnetic field in a closed path given by P is directly comparative to the quantity of current measured in the enclosed path. In the above case, the constant of proportionality is known as the permeability of free space.
T - Is the SI unit for measuring the magnetic field strength. In the above experiment, the magnetic field strength that will be measured will be much smaller; therefore, instead of using T (Tesla), the Gauss will be used to measure electric field strength. In most cases, Tesla (T) will be converted to Gauss.
When applying the Ampere's law, there is the need to consider an imaginary Amperian loop coiled in a rectangular shape which edges marked as abcd as indicated in figure 5. Along the path ab, the direction of the electric field is same as dl, therefore, the integrand will take the value BL. Along the paths da and bc, the fields take a perpendicular direction to the path B, dl will thus become zero. The path cd may be chosen to be a large distance from the solenoid where there is a zero electric field. In Ampere's law, the inclusion of the above observations will result in different scenarios.
The current circulating in the loop will represent the number turns or coils N along the length L that passes through the circular path multiplied by the current I from each coil. Therefore,
NI = IencBy definition, if the number of turns for each unit length is expressed as n = N/L, then the resulting field magnitude inside the solenoid is significant.
The above equation is used to obtain the field inside an infinitely long solenoid where there are closely spaced coils. In this experiment, there will be an opportunity to prove the validity of this equation for none ideal solenoid. To be more specific, there will be a measurement of the field outside and at the ends of the solenoid axis.
Testing the validity of the above solenoid equation can be carried out in two specific ways. Firstly, the variation of the solenoid length will be done while the constant value of the current flowing in each coil is kept constant. Consequently, there will be a variation of the current while keeping the length of the solenoid at a constant value. In both the two experiments, there will be determination and recording of flux density (B) using the Hall Probe. There will also be the determination of permeability of free space, denoted by m0.
During the experiment, there are two types of errors that might be anticipated. There may be systematic errors which are often caused by faulty in the instruments or if an instrument is not used correctly by an individual doing the experiment. There are random errors which may also be experienced in the experiment. The random errors may result from incorrectly calibrated balance which may interfere with the measurements taken during the experiment.
From the experiment, as the current increases, the magnetic field also increases. In other words, there is a linear increase in the magnetic field as current increases. From the equation, there is a linear proportionality between B and I. The graph shown in part I is consistent with the above prediction.
The magnetic field generated in the circuit is directly proportional to the coils made by the slinky. Additionally, the field increases significantly at all points.
Explanation for the Main Results of the Experiment
The results obtained from the experiment reflect the equation, B= m nI . From the equation, there is proportionality between B and I. Again, from the equation, B is proportional to n. The graph in part 1 and the data shown in part 2 are consistent with the above equation and the predictions that are associated with it.
The hypothesis formulated is relevant to the laboratory questions, it correctly answers the questions during the experiment. According to the experimenter, the increase in current at an interval of 0.2 A caused an increase in the magnetic field from 0.2 mT to 0.28 mT to 0.4 mT to 0.52 mT to 0.64 mT to 0.72 mT. In the subsequent part of the experiment, there was a decrease in the magnetic field from 0.78 mT to to0.73 mT to 0.72 mT to 0.7 mT to 0.69 mT.
The permeability constant can also be determined mathematically by examining the number of turns (n), current (I) and magnetic field (B). During the experiment, there was an estimation of 1.510-6TmA, as a permeability constant, a value which is closer to the actual value of1.2610-6TmA. Additionally, the movement of the magnetic field sensor towards the end of the slinky caused an increase in the magnetic field up to the half of the value at the ends. The above case is evidenced by the data 0.72mT recorded from the middle to 0.7mT and 0.69 mT at the end of the slinky. The decrease continues past the slinky ends.
Result Comparison with Other Previous Experiments
From this experiment, there are three possible sources of error. The rotation of the magnetic field sensor could have caused experimental errors as it was moved along the slinky. This error could have made the comparison of two experiments difficult since the sensor achieves various normal levels when rotated. The error could be eliminated by moving the magnetic field sensor along the roller track above the slinky that is entirely parallel to the slinky. An error could have also been experienced by the sensor that was continuously jumping; the behavior of the sensor could not give surety on whether the amount of current moving through the wire was being recorded. The above error in reading from the sensor could have resulted in skewed data. Using a current sensor with minimal jumping could facilitate the removal of the above error. Finally, the movement of the direction of the coil could have caused some error in reading during the experiment, a situation that could have influenced the magnetic field sensor. The sensor often has different normal at each point of the compass. This could have resulted in unreasonable comparisons in trials. Fixing the coil on the table to avoid movement could eliminate this error.
Giancoli, D. C. (2008). Physics for scientists and engineers. Pearson Education International.
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