Transcript
RYERSON UNIVERSITY
DEPARTMENT OF PHYSICS
LAB REPORT
FOR
PCS125SECTION
TITLE OF EXPERIMENT: Current Balance
EXPERIMENTERS:
(Full names and ID’s)
AUTHORS OF THIS REPORT:
EXPERIMENT PERFORMED ON (DATE): March 7th, 2012
REPORT SUBMITTED ON (DATE): March 14th, 2012
TA’S NAME: Marjan Razani
OBJECTIVE AND BACKGROUND:
When electrical current carrying a conductor is exposed to magnetic field it experience a magnetic force due to this field. However, when a conductor is charged, the charge will be disturbed all over the surface of the solid or object. Therefore, the purpose of this lab is to determine experimentally the magnetic force produced by electrical currents that are parallel, straight and at fixed separation by measuring its length, permeability of air and the current that pass through the conductor using DC power supply,current balance, weight and telescope. This lab; however, divided into two parts. Firstly, the magnetic force was calculated by using different weights (20mg, 40mg, 60mg, 80mg and 100mg) for each weight the current was increased gradually until the beam returned to its equilibrium position and then recorded the values of the weight and the current that required bring back the beam to its initial position. Secondly, we have computed the magnetic force by measuring the separation distance of the two bars by putting a coin on pan of the upper bar until the upper and lower bars are in contact and then recoding the new scale reading. Then, we have measured the length of the upper bar from its supporting edge and recorded its value. The following equations were used to calculate the data;
This equation shows the relationship between magnetic force, length and current;
F= (2kL/d) I2
Where L is the length of the current in m
F is the magnetic force in N
K is ?0/4
?0is permeability of vacuum
d is the separation of the conductor in m
I is the current in each wire in Ampere
The equilibrium separation distance of the two bars was computed by using this formula;
d0=Da/2b
Where D is the difference in reading scale
a is the mean distance between the knife edge to the bar
b is the distance from the mirror to the scale
In conclusion to all the equations shown above, the observation, graph and calculation will demonstrate each one in their own manner.
MATERIALS:
DC power supply
Scale
Current Balance
Telescope
Meter stick
Weight
DC power supply Meter Stick
Scale Current Balance
3631565147955
Telescope Weight (20mg) and coin
PROCEDURE:
In this experiment, we have computed the magnetic force by measuring the separation to the conductor, increase the current and using different weight values.
The apparatus was set up on the table in which the current balance mirror was
two meter distant from the scale by telescope. Then, the direction of the current carrying bar was run in North-South direction to minimize the effect of earth’s magnetic field.
The lift mechanism beam was observed in which the knife edges come cleared of their supports and then returned them to a particular position. The lift mechanism was used to gently lift the knife edges clear of their supports and then lower them back down. The frame was oscillated freely. The metal plate between the poles of damping magnets was distanced 2mm apart to prevent the magnets and the pole of the magnets from touching each other.
The leveling screws was adjusted in which the base of the apparatus firmly situated on the firm table. The counterpoise behind the mirror was adjusted until the frame comes to rest with the front horizontal bar millimeter above the stationary bar.
The thumb screw was noted on each front post to allow the end of the lower bar to be raised or lowered. Then, the thumb screw near the rear of the frame was noted to allow the end of the upper bar to be adjusted forward or backward. The lift mechanism was gently used to lift and replaced the knife edges in the proper place.
The telescope was directed at the mirror on the current balance. Then, the current balance base on the table was slowly rotated until the reflection of the scale was seen in the telescope. The beam lift was engaged and released gently to insure the knife edges still in their proper positions.
The cross hair of the telescope was focused, and then the main focusing of the telescoping was adjusted until the scale was seen clearly. Then, the scale was read as seen in the telescope with the beam of the current balance at rest in its equilibrium position. The separation of the two bars at equilibrium was adjusted.
Five 20mg weight was placed on the pan on the upper bar, and then the current was increased gradually until the scale reading indicates that the beam has returned to its equilibrium position. Then, the separation adjusted to insure that the required current was about 10 amps, but not more than 15 amps.
The current required to restore the beam to its equilibrium position for weight on the pan that ranging from 20mg to 100mg in 20mg increase was recorded.
The separation of the two bars at equilibrium was determined by noting the scale reading at equilibrium. Then, the upper bar was depressed by putting a coin on the pan until the upper bar was in contact with lower bar. The new scaling reading was noted. Thesimple geometry equation was used to calculate the openspace separation d0by this formula d0=Da/2b. Where D is the difference in scale reading, a is the mean distance from knife edges to the bar; b is the distance from the mirror to the scale.
The required center to center separation d, was obtained by adding the diameter to one bar to d0.
The value of d was checked by measuring it directly from the millimeter scale.
The length L of the upper front bar was measured from the center to center of its supporting bars.
The graph of F versus I2 was plotted. Then the values of F was noted from the weights of the masses was placed on the pan. The permeability of air was determined by finding and using the slope of the straight line graph. Then, the values of the permeability found and the know value for vacuum was compared.
OBSERVATIONS:
No of trials
Mass (mg)
F(N)
I (Amp)
I2 (Amp2 )
Trial 1
20
4.3
18.49
Trial 2
40
5.5
30.25
Trial 3
60
7.2
51.84
Trial 4
80
10.1
102.01
Graph 1: CURRENT SQUARED VS MAGNETIC FORCE
L = length of the upper front bar from the center to center of its supporting bars=26.5cm=0.265m
a = distance from the knife edge to the bar = 20.9cm = 0.209 m
b = distance from the mirror to the telescope = 88 cm = 0.88 m
CALCULATION:
Trial 1
F = mg = 9.81 m/s2 = N
I2 = (4.3)2 = 18.49 A2
Slope =
From the graph
slope 2kL/d = 8.7×10-6 NA2
D = difference in scale readings between the reference reading and the penny reading
= 6.4mm – 1.1 mm = 5.3mm = 0.0053m
d= D?a2b= 0.0053×0.2092 ×0.88=6.29×10-4m
d = D + d= 0.000629+0.0053 = 5.93×10-3m
F = and K = therefore:
= Where F/I2 represents the slope.
= 2?5.9×10-30.265 ?(8.7×10-6)
= 3.89? × 10-7
= 1.22 × 10-6 WbA?m
Percentage of error:
%error = ×100
= 4.00?×10-7 – (3.89?×10-7) 4.00?×10-7×100
= 3.0%
DISCUSSION AND RESULTS:
The amount of magnetic force a wire experiences is proportional to the product of magnetic field strength that the wire is subjected to, times the length of the wire, times the amount of current (in amps) the wire is carrying. Graph 1 shows that at a fixed position the force and current is directly related to the electric magnetic field. As more forces are being applied more current is required so, force between the two wires is proportional to the product of the two currents. From the graph calculated the slope to estimate the permeability of vacuum. And the permeability of vacuum is 3.89?×10-7with a percentage error 3%.
If two parallel wires have currents traveling in opposite directions, the magnetic fields generated by those currents between the wires will both point in the same direction, wires would repel each other. If two parallel wires have currents traveling in the same direction, the magnetic fields generated by those currents between the wires will both point in opposite directions resulting in the wires attracting each other
The possible errors in this experiment are the measurement took through the telescope. And also the image of the scale in the mirror, the image was not magnificent to measure the scale correctly
Possible methods of improving the experiment are to use standard measuring tools that can determine the distance between currents and record the voltage at the reference point.
CONCLUSION:
In conclusion, at a fixed position the force and current is directly related to the electric magnetic field. As more forces are being applied more current is required to keep the object at equilibrium. This experiment helps to study the magnetic forces produced by electric currents in wires that are straight and parallel. The magnetic force on a current-carrying wire is perpendicular to both the wire and the magnetic field with direction is found by the right hand rule.
REFERENCES:
Serway, Raymond A., and Jewett,Jr., John. Physics for scientists and engineers with modern physics. '7th ed'. Belmont,Ca: Lachina Publishing services, 2005.
"The Current Balance Manual." Ryerson University. Department of Physics. Mar. 2012.
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