1B40 Formal Report
Simon Hearn
Dr Crawford
UCL
DEPARTMENT OF PHYSICS & ASTRONOMY
FIRST YEAR LAB REPORT
MARCH 2001
EXPERIMENT E58: THE CURRENT BALANCE
PERFORMED BY SIMON HEARN, LAB PARTNER CAROLINE
BRIDGES
Abstract
The purpose of this investigation was to prove the relationship between the
force F on a wire length ℓ, carrying a current I, in a magnetic field B. This was
be done by performing two separate experiments, one to find the relationship
between F and I and the second to find the relationship between F and ℓ. The
observations concluded that the following relationship is true: F=BIℓ
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1B40 Formal Report
Simon Hearn
Dr Crawford
Introduction
When a current carrying conductor is subject to a magnetic field, it
experiences a force. It has been noticed that there is some relationship
between the magnitude of this force (F), the amount of current in the
conductor (I), the length of conductor subjected to the field (ℓ) and the
strength of the magnetic field (B), such that:
F=BIℓ
(1)
This experiment was designed to verify this relationship. A secondary
outcome was the measurement of the magnetic field. In order to do this two
experiments were performed. The first investigated the effect of changing the
current through the conductor, on the force experienced by the conductor,
while keeping the magnetic field strength and the length of conductor
constant. The second investigated the effect of changing the length of
conductor in the magnetic field on the force experienced, while keeping the
current and magnetic field strength constant.
Experimental Method
In order to measure the force on the conductor a balance was used. This is
basically a square loop of wire, pivoted on two electrical contacts and
balanced using a counterweight, this was connected up (at the two contacts)
to a steady current supply and an ammeter (see fig 1).
Fig1: the circuit set up.
***NO IMAGE***
Page 2 of 5
1B40 Formal Report
Simon Hearn
Dr Crawford
From fig 2, it can be seen that when a current is passed through the circuit,
the force on the part of the conductor within the magnetic field will be directed
upward. This force can be countered by sliding a mass (rider) along the wire,
so that the torque on the system due to the mass equals the torque due to the
magnetic field, this can be show using the following equation:
Fx1 = mgx2
(2)
This also means that the force on the conductor is directly proportional to the
position of the rider along the wire (x2).
Fig 2: the forces on the conductor ***NO IMAGE***
For the first experiment, the current was increased in intervals, and at each
value the rider was re-positioned so that the wire was horizontal. The current
was graphed against rider position (see graph 1). For the second experiment,
the magnets were slid along in intervals, so that the length of conductor in the
magnetic field varied. At each interval the length on conductor subject to the
magnetic field and the corresponding new rider position was recorded. This
was repeated three times, to eliminate any errors in reading the rulers. The
average rider position and the length of conductor in the field was plotted (see
graph 2).
Page 3 of 5
1B40 Formal Report
Simon Hearn
Dr Crawford
Experimental Results
The following graphs were plotted by entering the pre-recorded data, into
Average Rider Position (mm)
Microsoft Excel.
50
45
40
35
30
25
20
15
10
5
0
0
10
20
30
40
50
Length on Conductor in Field (mm)
Graph 1: Current against rider position, with a computed best-fit line.
40
Rider Position (mm)
35
30
25
20
15
10
5
0
0
0.5
1
1.5
2
2.5
Current (A)
Graph 2: Length of conductor against average rider position, with a computed
best-fit line.
Page 4 of 5
1B40 Formal Report
Simon Hearn
Dr Crawford
Analysis of Results
From equations (1) and (2), we get:
BIℓx1 = mgx2
(3)
Using this and the gradient of graph 1 (m1) we get:
B = m1 x mg / (ℓx1)
Where :
(4)
m= mass or rider = 1.78 ± 0.001 g
ℓ = length of conductor = 4.5 ± 0.05 cm
x1= 10.10 ± 0.05 cm
m1= gradient of graph 1. = 0.0177± 0.000456
This gives:
B = 0.0681 ± 0.0019 T
Using equation (3) and the gradient of graph 2 (m2) we get:
B = m2 x mg / (Ix1)
Where :
(5)
I = current travelling through conductor = 2.01 ± 0.005 A
m2= gradient of graph 2. = 1.023 ± 0.033
This gives:
B = 0.0880 ± 0.0029 T
The magnetic field of the magnet was measured using a gauss meter, it was
found to be 0.0879 ± 0.0009 T.
Conclusions
Graph 1 shows distinctly that the current is directly proportional to the rider
position, and hence the force on the wire. Graph 2 shows that the length of
conductor in the magnetic field is directly proportional to force on the
conductor. This verifies equation (1). The second estimate of the magnetic
field strength is very precise and accurate; the first estimate turned out to be
inaccurate, but precise. This probably means that different magnets were
used for each experiment so I can ignore the first result. I can conclude that
the experiment was very accurate, and gave an indirect reading that was
within the error of the actual value.
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