Magnetic Force on
Current Carrying Wires
Curtis H. Choi
Joseph Wassei
Jonathan Po
Physics 2B Laboratory Presentation
Costantino
Las Postias College
April 25,2003.
Background

History of Magnetism

Magnesia


Chinese


“Lodestones” attract pieces of iron
Compasses made of lodestones
William Gilbert (1500’s)
Artificial magnets, by rubbing lodestone and iron
 “electrics” attracting various materials (Amber (G))
 Static electrical attraction to a magnetic attraction


Electrical attraction may be transmitted through an object
Background

History of Magnetism cont.

Hans Christian Ørsted (Physicist)


Accidental discovery re-linking electric
and magnetic theory
Ampére (Mathematician)

Source of magnetic field is electric current,
as the source of an electric field is an
electric charge

Magnetic field (B) around a wire is
proportional to the current flowing through
the wire
 Right hand rule
Two current-carrying wires attract/repel
depending on direction of current

Theory

Interaction between a moving charge and a
magnetic field can be described as followed:
F=qvBsinθ
(Eqn. 1)
q= magnitude of moving charge, v= velocity B= magnetic field

Extended using cross-sectional area A and Length
L carrying current I
F= qvdB
vd=drift velocity
(Eqn. 2)
Theory

Since V=AL & the number of carriers=nAL the magnitude of
total magnetic force on a wire with length L is:
F=(qvdB)(nAl)

Since I=nqvdA, “F” may be expressed:
F = ILBsinθ = ILB

(Eqn. 3)
(Eqn. 4 & 5)
Assumptions made in our experiment: none of the electrons escape
into the atmosphere, also neglect all forces on magnetic holder
other than gravitation and electrical (magnetic)
Experimental Arrangement
•Obtain the following equipment
•Basic Current Balance and
Accessory
•Quadruple-Beam Gram
Balance
•DIGI Power Supply
•DMM
•Patch cords
Experimental Arrangement
Assemble apparatus
(used in Part A ~ C)
Experimental Arrangement
Part A
• Assemble apparatus
• Determine and record the mass of the
magnet holder and magnets with no
current flowing (m0).
Magnet holder
Magnets
Experimental Arrangement
Part A
• Assemble apparatus
• Determine and record the mass of
the magnet holder and magnets with
no current flowing (m0).
• Measure the new “mass” of the
magnet assembly in different current
settings (0.5amp ~ 2.0amp increasing
the current in 0.25 increments).
Experimental Arrangement: Part B
Part B
• Determine and record the
length of the conductive foil
on the current loop (L).
• Determine the new “mass”
of the magnet assembly at
2.0amps current and record
it as m(L).
• Subtract m0 from m(L) and
record as F(L).
•Repeat the above steps with
all the other current loops.
Experimental Arrangement
Part C
• Mount a single magnet in the
center of the holder.
• Determine the mass of the
magnet assembly without current
flowing and record as m(n).
•Set the current to 2.0 amps.
Determine the new “mass” of the
magnet assembly and record it as
m(n,c).
•Subtract m(n) from m(n,c) and
record the difference as F(n).
Experimental Results


This apparatus was used in Part
A: Force vs. current, Part B,
Force vs. length of wire, and
Part C: Force vs. magnetic field.
Magnetic holder
weight(m0)= .1614 Kg
Main unit
Magnetic
holder
Current
loop
Quadruplebeam
balance
Part A: Force vs. Current
Force vs. Current
• The equation of the graph is
Y= .0002x - 2E-6.
m0= .16135 Kg
•The slope of the line was found to
be .0002 L*T.
•The slope of the line is LB from the
equation (F/I)=LB.
m (c)
(kg)
0.5
1.615E-01
1.000E-04
0.75
1.615E-01
1.300E-04
1
1.615E-01
1.900E-04
1.25
1.616E-01
2.400E-04
1.5
1.616E-01
2.800E-04
1.75
1.617E-01
3.400E-04
2
1.617E-01
3.750E-04
(N)
Force vs. Current
y = 0.0002x - 2E-06
R2 = 0.9955
4.000E-04
3.500E-04
3.000E-04
F(c) (N)
•This equation tells us that if the
current increases so does the force
acting on the wire.
F(c)= m(c)-m(o)
I
(A)
2.500E-04
2.000E-04
1.500E-04
1.000E-04
5.000E-05
0.000E+00
0
0.5
1
1.5
Current (A)
2
2.5
Part A: Force vs. Current
Force vs. Current
5.0E-04
F(c) (N)
4.0E-04
F = 2.xx(10-4) I - 2.00(10-6)
R2 = 0.9955
3.0E-04
2.0E-04
1.0E-04
0.0E+00
0
0.5
1
1.5
Current (A)
• The equation of the graph is F = s*I + F0
•The slope of the line is s = B*L = 2.xx(10-4) N/A
• For L = 2.00 cm, B = 0.076 T
2
2.5
Part B: Force vs. Length of Wire
• The equation of the graph is
Y=.0432x - .0004.
Force vs. length
m0= .16135 Kg
L
(m)
m(l)
F(l)=m(l)-mo
0.02100
1.617E-01
3.750E-04
0.03700
1.623E-01
1.325E-03
•The slope of the line is IB from the
equation (F/L)=I*B.
0.02500
1.619E-01
5.500E-04
0.01100
1.616E-01
2.800E-04
0.03100
1.625E-01
1.012E-03
•As length of wire increases so
does force acting on the wire.
0.04100
1.628E-01
1.430E-03
•The slope is .0432 A* T.
•The current was 2.0 Amps
Force vs . Le ngth
•Equation:
y = 0.0432x - 0.0004
R2 = 0.923
1.600E-03
1.400E-03
•slope=B*I
F(c) (N)
•B= .0432/2= .0216 T
1.200E-03
1.000E-03
8.000E-04
6.000E-04
4.000E-04
2.000E-04
0.000E+00
0.000E+00
1.000E-02
2.000E-02
3.000E-02
Le ngth(m )
4.000E-02
5.000E-02
Part C: Force vs. Magnetic Field
•The equation of the graph is y=
7E-7x + 4E-5.
Force vs. Magnetic Length
m(n)= .099745 Kg
•The slope of the graph is 7E-7 N
per magnet.
• As the number of magnets inc.
so does the Force in the
magnetic field.
n
m(n)
m(n,c)
F(n,c)=m(n,c)-m(n)
1
9.975E-02
9.984E-02
9.500E-05
2
1.120E-01
1.122E-01
1.800E-04
3
1.245E-01
1.247E-01
2.500E-04
4
1.367E-01
1.370E-01
3.100E-04
5
1.490E-01
1.493E-01
3.300E-04
6
1.613E-01
1.618E-01
4.500E-04
Force vs. Magnetic Field
5.000E-04
y = 7E-05x + 4E-05
R2 = 0.9722
Force(N)
4.000E-04
3.000E-04
2.000E-04
1.000E-04
0.000E+00
0
1
2
3
4
Number of magnets(n)
5
6
7
Errors

Possible errors in this
experiment are:

The quadruple-beam
balance was not
calibrated correctly.

Length of the
conductive wire
measured might have
been measured
incorrectly.
Conclusion

The magnetic field was found to be .0216 T using the equation
slope = B*I

It was found that as the current, number of magnets, and the
length of the conductive foil inc so does the force in the magnetic
field.
Magnetic Force on
Current Carrying Wires
Curtis H. Choi
Joseph Wassei
Jonathan Po
Physics 2B Laboratory Presentation
Costantino
Las Postias College
April 25,2003.