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Magnetic field around a conductor

Extracts from this document...

Introduction

Fredrik Hansen IB1A

IB Tingvallagymnasiet Karlstad

Physics Department

Fredrik Hansen

Mail: f_ananas@hotmail.com

Laboratory experiment:

Magnetic Field around a Conductor

IB Physics Higher Level

laboratory experiment report

by Fredrik Hansen

class: IB1A

supervisor: Anna Malmberg

conducted: 2009-05-29

written: 2009-07-27

Contents

Introduction

Symbols

Aim

Research question

Independent variable

Dependent variable

Controlled variables

Hypothesis

List of material

Preparation

Method

Analysis

Conclusion        6

Evaluation

Introduction

A conductor induces a magnetic field around itself while carrying a current. This magnetic field has the same properties as normal magnetic field in all aspects except that the field is oriented in a closed circle around the conductor following the right hand rule.

Symbols

In this experiment following symbols are used:

B = magnetic field [T]

I = current [A]

V = voltage [V]

R = resistance [Ω]

r = radius [m]

µ0 = permeability of free space (constant) [4π*10-7 TmA-1]

Aim

The scientist is supposed to investigate the relationship between current and magnetic field in a conductor by running a varying current through a circuit and measure the magnetic field induced by it. Furthermore the practical skills in the subject of the magnetism and electrical currents should improve.

Research question

How is the magnetic field (B) dependant on the current (I)?

Independent variable: Current (I)

Dependent variable: Magnetic field (B)

Controlled variables:

  • Radius (r)
  • Permeability of free space (µ0)

Hypothesisimage00.jpg

...read more.

Middle

        A value for the relationship between I and B can be found through processing the raw data found and creating a graph of it.

Processing the data into the universal formula for a linear graph (y=mx+c) B can represent the y value and I can represent the x value, making the m value represent m=µ0/2πr. (see next page for graph) solving this formula for µ0 makes:

        µ0 = maverage2πr

        µ0max = mmax slope2πr

        µ0min = mmin slope2πr

Notice that the real value of m is only 1/1000 of the value presented in the graph as mT is used as unit in the data table. Furthermore r is kept constant at 1 cm.

Trial #1

Thus           m = 2.14*10-5 TA-1,              mmax slope = 2.39*10-5 TA-1              and               mmin slope = 1.99*10-5 TA-1image05.jpg

µ0 = (2.14*10-5)*2π*0.01 = 4.28π*10-7 TmA-1

µ0max = (2.39*10-5)*2π*0.01 = 4.78π*10-7 TmA-1

µ0min = (1.99*10-5)*2π*0.01 = 3.98π*10-7 TmA-1

inaccuracy = (max-min)/2

(4.78π*10-7-3.98π*10-7)/2 = 4π*10-8 TmA-1

Thus the calculated value for µ0 is:

4.28π*10-7 TmA-1 ±4π*10-8 TmA-1

        The V/I relationship also known as the resistance of the circuit is controlled by the table to the right. As is implied in this table the resistance remained ohmic as it should.

image06.jpg

Trial #2image07.jpg

In Trial #2 the radius was kept constant at 1.

...read more.

Conclusion

-7 TmA-1. The deviation of the calculated values for the permeability of free space in the first two trials implies that there is a systematic error. However the third trial is very precise without such a systematic error.

        Both the fact that the graph is linear and that the calculated value supports the hypothesis as the real value lies within the inaccuracy. Also the fact that the repeated data collection is accurate supports known theory and the hypothesis.

Evaluation

        The evaluation seems reasonable as the results were close to the real value all implying that the lab was well designed and executed. However the magnetometer was very sensitive to external factors and made several resets of the scale were necessary before a data collection could be performed. The inaccuracy of the readings of the magnetic field made the error bars in the graph unnecessarily large.

        The fact that the y intercept is not zero in the first two graphs suggests a minor systematic error however the error remains unidentified. The repeated measurement and calculation of average removes the unavoidable difficulties in making accurate measurements every time.

        There are not many ways this laboration can be improved, except for finding the systematic error, as it gave a clear and correct value.

Tingvallagymnasiet Physics Department

...read more.

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