Magnetic Fields

Magnetic Fields

PHY 114 Lab Report

10/23/2013

Abstract:
The purpose of this experiment was to surrounding a magnet there is a magnetic field. The magnetic field is analogous to the electric field that exists in the space around electric charges. Like the electric field, the magnetic field has both a magnitude and a direction. The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. Since electric current is a flow of charge the behavior of a compass needle in the presence of current carrying elements indicates that moving charges produce magnetic field. For a loop of wire consisting of N turns wound close together to form a flat coil with a single radius R, the magnetic field resembles the pattern of a short bar magnet, and at the center of the coil its magnitude is B=N. The direction of the magnetic field at the center of the wire loop can be determined with the help of RIGHT-HAND-RULE. If the thumb of the right hand is pointed in the direction of the current and the curled fingers are placed at the center of the loop, the fingers indicate the direction of the magnetic field.
For a square coil equation (1) has a slightly different constant. In this case the formula for the magnetic field in the center of the coil is:

Objective: The objective of this lab was to study magnetic fields generated by a square shape current carrying coil.
Procedure:
We have to measure the length of the side of the coil. The square coil unit has a compass responds only to the horizontal component of the earth magnetic fields.
Connect the circuit and then set the coil first so that the compass points perpendicular to the plane of the coil. Cause a current to pass through the coil and observe the behavior of the compass. Now turn the coil 180o around and again apply a current to the coil. Set the coil unit in such a way that the compass needle points parallel to the plane of the coil. Increase the current and observe the deflection of the needle. The compass needle aligns itself in the direction of a net magnetic field, which is a vector sum of the horizontal component of the earth’s magnetic field and the field generated by the coil.

Take measurements of the needle deflection angle θ with the plane of the coil vs. current I in the coil. In Graphical Analysis make a plot of θ vs. I. Is this graph linear? Now, plot tanθ vs. I (be sure the preferences in GA are set for angles in degrees). We have tanθ = Bcoil /Bearth. Since Bcoil is expected to be proportional to the current in the coil, so tanθ =  ·I/Bearth. This can be rewritten as tan =MI where M =  /Bearth = constant. We made direct measurements of the magnetic field strength in the center of the coil vs. current in the coil using a Hall effect sensor. For the experiment conditions the detector sensitivity has to be set to × 100.
Then the sensor measures the B field perpendicular to the white dot in either the axial or radial direction. The compass needle is made of magnetic material and when it turns it produces a changing component of magnetic field, which affects your measurements adding undesirable nonlinearity. Such situation has to be avoided.
The sensor has a zero offset and the reading at no current does not necessarily indicate the value of the ambient field. The pre-set experiment file is preset to record magnetic field measured by the sensor as a function of current in the coil. With no current in the circuit (power supply off, voltage adjustment knob at 0) press “Start” in the experiment file, then “Tare” on the magnetic fields sensor, next turn on the power supply and slowly keep increasing the output voltage from the power supply. Stop the data acquisition at I  0.95 A. Apply the linear fit to your data and compare the slope with the theoretically predicted value from equation (2).

DATA:
Tan 0 = MI
M= 3.248
Tan 45/ 3.248= 0.3078 A
1 gauss = 10e-4 T
N2
20 2 4 x e -7 ( T mA ) = 1.148 e-4 ( 0.098 )
Error percent:

Results:
Magnetic field strength (100x)
Current 1.072 A
7 gauss liner fit m ( slope ) 1.23+- 0.016 b ( Y intercept ) -0.0553 +- 0.010 r 0.994
Mean square Error 8.94E-4
Root MSE 0.0299
Angels vs. Current
Liner fit for Data set Tan Angle
Y=mx+b
M( slope ) 3.248
B(y-intercept) 0.05547
Correlation 0.9991
RMSE 0.02697
For angle= 45 deg, I=1/M=0.3079 A

Discussion:
To begin, In this experiment we used a computer interface with current and magnetic field sensors, DC power supply, and square shape coil unit ( 20 turns ) with a compass mounted in the center.
The experiment, we found the experimental results agree extremely well with the theoretical prediction that the magnetic field strength B at the center of a circular coil is proportional to the current I in the coil. The deduced number of turns N in the coil also agrees with our estimate by counting. When B is measured as a function of x at fixed I, the deduced N is much bigger. We expect the error in this estimate of N to be bigger because it relies on the accurate estimation of the position of the center of the coil. The fact that the estimated m = −1.48 is close to the theoretical value of -1.5 indicates that we have located the center of the coil fairly accurately.
We study the two coils configuration. The experimental results show correct qualitative behavior both when current is flowing in the same and opposite sense in the coils. The data also agrees quantitatively with the theory within the uncertainties of the experiment, except for a few data points at large negative x.

Conclusion: The objective of this experimental was to study magnetic field generated by a square shape current carrying coil. We have studied the magnetic field generated by different current configurations involving coils of wire. The experimental results agree quantitatively with the theoretical predictions within the uncertainties of the experiment. Reasonable values for the number of coils in each configuration are deduced from our experimental data.