Bil
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Name : Adam Okoe Mould Title : Magnetic Force on a Current-Carrying Conductor Criteria : DCP, CE Aim : To determine the relationship between current and the force on a conductor placed in a magnetic field. Raw Data Current / A ± 0.05A Mass /g ± 0.01g 0.50 0.05 0.80 0.10 1.20 0.14 1.60 0.19 2.20 0.25 2.90 0.33 Observation As the current increased the mass increased. However, the current readings were quite unstable. Processed Table Of Results Current / A ± 0.05A
Mass /g ± 0.01g
0.50 0.80 1.20 1.60 2.20 2.90
0.05 0.10 0.14 0.19 0.25 0.33
Calculations ∆Current = limit of reading on scale ÷ 2 = 0.1 ÷ 2 ∆Mass = limit of digital reading = ±0.01g Mass /kg = Mass / g × 1000 ∆Mass /kg = ∆Mass / g × 1000 = 0.01 × 1000 = ±0.00001kg Force on Coil = Mass/kg × 9.81 ∆ Force on Coil = ∆Mass/kg × 9.81 = 0.00001 × 9.81 = ± 0.0001 N
Mass /kg ± 0.00001kg 0.00005 0.00010 0.00014 0.00019 0.00025 0.00033
Magnetic Force on coils /N ± 0.0001N 0.0005 0.0010 0.0014 0.0019 0.0025 0.0032
Analysis of Results The accepted relationship between the force on a coil and the current is as shown below ; F = BILNSin(θ) Where F = Force experienced by the coil B = Magnetic field strength I = Current flowing through coil L = Length of coil in the magnetic field N = Number turns of coil θ = the angle between the current flowing through the conductor and the magnet coil This formula implies that when the magnetic field strength, the length of the coil and the angle between the current and the magnetic coil are kept constant, the force experienced by the coil is supposed to directly proportional to the current flowing through the coil. Hence a graph of current against magnetic force on coil will be plotted to observe the relationship between current and force.
Graph of current against magnetic force Comment on graph and results • As the current increased, the force on the coil correspondingly increased • The line of best fit plotted through the graph shows that the current in the co
3
y
2.5
Minimum Slope 2
1.5
urent/A C
Line Of Best Fit
1
0.5
Maximum Slope
x
0.00020.00040.00060.0008 0.001 0.00120.00140.00160.0018 0.002 0.00220.00240.00260.0028 0.003 0.00320.0034
Force on the coil / N •
il is directly proportional to the force on the coil as the line of best fit is a straight line passing through the origin. The intercept of the maximum and minimum slopes O.22 and 0.14 from the origin are indicative of the fairly large uncertainty due to the measuring apparatus. Hence the points were scattered above and below the line of best fit. But as sufficient range of data was collected a good line of best fit made up for this large uncertainty.
List of possible sources of error 1. Since the setup was recently used, the current in the circuit had previously heated to the coils. Therefore, when experiment was performed the current would have been affected by the rise in temperature. List of improvements 1. Ensure that the set up being used has not been used within the 30 minutes. This will ensure that the temperature in the coil has dropped to that of the room temperature. Conclusion The current in a coil placed in a magnetic field is directly proportional to the force experienced by the coil as the line of best fit was a straight line that passed through the origin within the given error bars when a graph of current against force was plotted. The experiment was susceptible to large uncertainties due to the uncertainties in the measuring apparatus. However, since enough data was collected the errors were overcome.
8
y
7 6 5 4 oltage/ V
3 2 1
x -0.05
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Current / A
Comment on Graph and Processed Results • • •
The graph shows that as the voltage increases, the current in the circuit reduces. The results are fairly precise as the points are scattered fairly close to the line of best fit. There was only one random error which was in the first reading.
Determination of e.m.f and Internal resistance of battery
From the line of best fit the gradient is -4.23 VA-1 and the intercept is 7.60 Gradient = -4.227 But Gradient = -r Therefore -r = -4.23 r = 4.23 Ohms Hence, the internal resistance of the battery is 4.23 Ohms Intercept = 7.60 But Intercept = e.m.f Therefore e.m.f = 7.60 Therefore the e.m.f of the battery is 7.60 V Measured e.m.f - e.m.f derived from graph × 100 Measured e.m.f 8.5 - 7.6 × 100 = 8.5 = 10.6 % This percentage error of 10.6 % in the value of the e.m.f shows that the experiment was not very accurate but only fairly accurate. Percentage error of e.m.f =
Conclusion Based on the graph of voltage against current, the internal resistance of the battery is 4.23 Ohms and the e.m.f is 7.60 V. The experiment was fairly accurate as there was a percentage error of 10.6 % for the value of the e.m.f. Sources of Error 1. During the performance of the experiment, the batteries their energy drained out rapidly. This may have caused some errors in the experiment. 2. As the experiment progresses, the heat produced by the flow of current could have added further errors. Improvements to the Investigation 1. High quality batteries should be used so that the energy in the battery will last for the whole duration of the experiment. 2. To minimize the generation of heat in the wires uses thicker wires.
Mass /g ± 0.01g
0.50 0.80 1.20 1.60 2.20 2.90
0.05 0.10 0.14 0.19 0.25 0.33
Calculations ∆Current = limit of reading on scale ÷ 2 = 0.1 ÷ 2 ∆Mass = limit of digital reading = ±0.01g Mass /kg = Mass / g × 1000 ∆Mass /kg = ∆Mass / g × 1000 = 0.01 × 1000 = ±0.00001kg Force on Coil = Mass/kg × 9.81 ∆ Force on Coil = ∆Mass/kg × 9.81 = 0.00001 × 9.81 = ± 0.0001 N
Mass /kg ± 0.00001kg 0.00005 0.00010 0.00014 0.00019 0.00025 0.00033
Magnetic Force on coils /N ± 0.0001N 0.0005 0.0010 0.0014 0.0019 0.0025 0.0032
Analysis of Results The accepted relationship between the force on a coil and the current is as shown below ; F = BILNSin(θ) Where F = Force experienced by the coil B = Magnetic field strength I = Current flowing through coil L = Length of coil in the magnetic field N = Number turns of coil θ = the angle between the current flowing through the conductor and the magnet coil This formula implies that when the magnetic field strength, the length of the coil and the angle between the current and the magnetic coil are kept constant, the force experienced by the coil is supposed to directly proportional to the current flowing through the coil. Hence a graph of current against magnetic force on coil will be plotted to observe the relationship between current and force.
Graph of current against magnetic force Comment on graph and results • As the current increased, the force on the coil correspondingly increased • The line of best fit plotted through the graph shows that the current in the co
3
y
2.5
Minimum Slope 2
1.5
urent/A C
Line Of Best Fit
1
0.5
Maximum Slope
x
0.00020.00040.00060.0008 0.001 0.00120.00140.00160.0018 0.002 0.00220.00240.00260.0028 0.003 0.00320.0034
Force on the coil / N •
il is directly proportional to the force on the coil as the line of best fit is a straight line passing through the origin. The intercept of the maximum and minimum slopes O.22 and 0.14 from the origin are indicative of the fairly large uncertainty due to the measuring apparatus. Hence the points were scattered above and below the line of best fit. But as sufficient range of data was collected a good line of best fit made up for this large uncertainty.
List of possible sources of error 1. Since the setup was recently used, the current in the circuit had previously heated to the coils. Therefore, when experiment was performed the current would have been affected by the rise in temperature. List of improvements 1. Ensure that the set up being used has not been used within the 30 minutes. This will ensure that the temperature in the coil has dropped to that of the room temperature. Conclusion The current in a coil placed in a magnetic field is directly proportional to the force experienced by the coil as the line of best fit was a straight line that passed through the origin within the given error bars when a graph of current against force was plotted. The experiment was susceptible to large uncertainties due to the uncertainties in the measuring apparatus. However, since enough data was collected the errors were overcome.
8
y
7 6 5 4 oltage/ V
3 2 1
x -0.05
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Current / A
Comment on Graph and Processed Results • • •
The graph shows that as the voltage increases, the current in the circuit reduces. The results are fairly precise as the points are scattered fairly close to the line of best fit. There was only one random error which was in the first reading.
Determination of e.m.f and Internal resistance of battery
From the line of best fit the gradient is -4.23 VA-1 and the intercept is 7.60 Gradient = -4.227 But Gradient = -r Therefore -r = -4.23 r = 4.23 Ohms Hence, the internal resistance of the battery is 4.23 Ohms Intercept = 7.60 But Intercept = e.m.f Therefore e.m.f = 7.60 Therefore the e.m.f of the battery is 7.60 V Measured e.m.f - e.m.f derived from graph × 100 Measured e.m.f 8.5 - 7.6 × 100 = 8.5 = 10.6 % This percentage error of 10.6 % in the value of the e.m.f shows that the experiment was not very accurate but only fairly accurate. Percentage error of e.m.f =
Conclusion Based on the graph of voltage against current, the internal resistance of the battery is 4.23 Ohms and the e.m.f is 7.60 V. The experiment was fairly accurate as there was a percentage error of 10.6 % for the value of the e.m.f. Sources of Error 1. During the performance of the experiment, the batteries their energy drained out rapidly. This may have caused some errors in the experiment. 2. As the experiment progresses, the heat produced by the flow of current could have added further errors. Improvements to the Investigation 1. High quality batteries should be used so that the energy in the battery will last for the whole duration of the experiment. 2. To minimize the generation of heat in the wires uses thicker wires.
