Figure 2: The experimental setup
The current balance was set up on the laboratory bench with the current carrying bars extending in a north-south direction to eliminate the effect of the Earth’s magnetic field. The distance from the mirror to the scale was approximately 2 meters. The beam lift mechanism was designed to raise the beam, which caused the knife edges to come clear of their supports and then to return them to a certain position. This mechanism was used to return the knife edges back to their initial position in case they moved a little during the experiment. Using this mechanism to raise the knife edges clear of their supports and then lowering them back down caused the frame to oscillate freely. There was not any contact between the damping magnets and the metal plate which was between the poles of the damping magnets.
By adjusting the levelling screws, the base of the apparatus was firmly situated on a firm table. The counterpoise behind the mirror was adjusted until the frame came to rest with the front moving bar a few millimetres above the fixed bar. In addition, the counterpoise below the mirror could be adjusted to make the period of the oscillations of the frame 1 to 2 seconds.
There were two thumb screws on each front post of the balance which allowed for the fixed bar to be raised or lowered at each end. Likewise, thumb screws near the back of the frame allowed for the moving bar to be adjusted forward or backward at each end. By using theses thumb screws the bars could be placed parallel to one another. The telescope was aimed at the current balance mirror, but it was not focused on the mirror. While one person was looking through the telescope another person was able to slowly move the current balance base on the table until a reflection of the scale was seen in the telescope. The adjustment screw behind the mirror could be used to change the angle of tilt of the mirror in order to make it easier for the scale to be seen in the mirror.
First the cross hairs of the telescope were focused, and then the main focus of the telescope was adjusted so that the scale could be seen clearly. Once the bars were at rest, the balance was in its equilibrium position. This position was seen on the scale thorough the telescope and was recorded. Five 20-mg weights, from 20 mg to 100 mg, were placed on the pan on the upper bar at five steps, and at each step the current was gradually increased to bring the moving bar back to its equilibrium position. The current was recorded for each of five weights. The current did not exceed 15 amps.
In order to calculate the separation of the two bars at equilibrium, the difference in the scale readings (D), the distance between the knife edge and the bar (a), the bar diameter (r), and the distance from the scale to the mirror (b) were needed. The difference in the scale readings was just the difference between the scale reading at the equilibrium position, and the scale reading when a coin was placed on the pan. A calliper was used to measure the bar diameter (r). The distance between the knife edge and the bar (a) and the distance from the scale to the mirror (b) were measured using a measuring tape. In addition, the length of the upper front bar from center to center of its supporting bars (L) was measured with the measuring tape.
Bar diameter (r) = 3.5 mm
Distance from the scale to the mirror (b) = 179.50 0.05 cm
The distance between the knife edge and the bar (a) = 20.70 0.05 cm
The overlapping length of current carrying conductors (L) = 26.30 0.05 cm
The difference in the scale readings (D) = 15.5 cm 8.7 cm = 6.80 0.05 cm
Table 1
Calculations, Graphs and Results:
The following calculations were used to determine the value of K and as a result the value of experimentally. For determining the value of K the following equations were used:
First the slope was determined by plotting against and finding the slope of its line of best fit. F is the value for the weights of the masses placed on the pan in the experiment (F=mg). I is the current in each wire in amperes.
Table 2 (g = )
Graph 1
Now, the value of K can be calculated by using the obtained values.
Discussion of Results And Conclusions:
It was observed in this experiment that a magnetic force of repulsion exists between two parallel current carrying conductors with currents in the opposite directions. This force is a function of the permeability of free space, the current in each conductor, the separation of conductors and the overlapping length of conductors. It was observed in the experiment that by increasing the current in bars, the magnitude of the magnetic force increases. The value obtained for the permeability of free space ( in the experiment was close to the actual permeability of free space. The calculated value for the permeability of free space had a deviation percent of 2%, which is a good result, but it could be improved by eliminating sources of error. There were several sources of error in this experiment. One source of error lies in using the measuring tape for measuring the distance between the knife edge and the bar (a) and the distance from the scale to the mirror (b), which involves reading error. This kind of error could be reduced by using an electronic device which could help in measuring the precise values of distances. Another source of error in this experiment was the effect of the Earth’s magnetic field on the separation of the conductors. Moreover, since the numbers being measured are very small, the friction that exists on the pivots where the bars are connected should be one of the main sources or errors. Sources of errors can be reduced in the following ways: performing the experiment many times, performing the experiment under the effects of a vacuum if possible, and minimizing the friction on the pivots of the bars.
The value of the permeability of free space that was calculated in this experiment was close to the actual one. In reality other factors (sources of error); mentioned above, have to be taken into account.
References:
- PCS 125 Lab Manual (2008 fall), Department of Physics, Ryerson University, Toronto.