Measuring earth’s magnetic field from thedeflection of a compass needle∗

Mohsin Raza Khan, Haseeb Ahmad, Muhammad Umar Hassan andMuhammad Sabieh Anwar

LUMS Syed Babar Ali School of Science and Engineering

November 23, 2018Version 2018 -1

This experiment aims to find the horizontal component of earth’s mag-netic field using a simple experiment. The experiment involves the investi-gation of the combined effect of the magnetic fields produced by the earthand a current carrying multi-turn coil. With the help of graphs, students areexpected to study the relation of current through the coil and the magneticfield that it generates. Furthermore, magnetic fields measured at differentdistances will provide insight to the distance dependence of the magneticfield.

KeywordsMagnetic field · · Tangent galvanometer · Hall effect · magnetic torque ·

Magnetic dipole moment

Essential pre-lab reading:

1. Fundamentals of Physics, 9’th edition, Halliday, Resnick and Walker,(Section 29–6).

2. Conceptual Physics, 10’th edition, Paul G Hewitt, (Chapter 24, page469–470).

∗No part of this document can be re-used without explicit permission from Dr. Muham-mad Sabieh Anwar. This experiment is distributed under the Commons Creative CC-BY-SA license.

1

1 Experimental Objectives

After the completion of this experiment, you should be able to understandthat,

1. a current produces a magnetic field,

2. the Hall effect can be used to measure the magnetic field,

3. determine the resultant of two vectors, and

4. how to make graphs and fit data.

2 Introduction

The earth, just like many other planets, possess a magnetic field whose shaperesembles that of a bar magnet. The Magnetic dipole is a fundamentalentity in magnetostatics just like a point charge is in electrostatics. A barmagnet is an approximate magnetic dipole. The magnetic field lines of abar magnet form a closed loop as shown in the accompanying figure. Themagnetic dipole moment, by convention, is a vector pointing from the southto the north pole. We can find the direction of the field at any point inspace around the magnet by taking the tangent at the field line at thatparticular point. A freely suspended magnet tries to align with the north.For example, the compass needle also aligns with earth’s magnetic field andhas been used for millenniums by explorers and seafarers for navigating thenooks and corners of the globe. This lab exercise is a simple undertaking inquantitatively estimating the magnitude of the terrestrial field.

Q 1. We know that motion of electric charges causes magnetism, butwhat is moving inside a household permanent bar magnet?

2.1 The Hall Effect and Hall sensors

The Hall effect was discovered by Dr. Edwin Hall in 1879 while he wasa Ph.D. student.. When a current-carrying conductor is placed inside aperpendicular magnetic field, a voltage will be generated perpendicular toboth the current and the magnetic field. This principle is known as the Hall

2

Figure 1: Conceptual illustration of earth’s magnetic field. This imageis taken from http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/

MagEarth.html

.

effect. The Hall voltage, VH is proportional to the magnetic field B andcurrent, I,

VH = CBI

where C is a constant of proportionality. The phenomenon of Hall effect isillustrated in Figure 2. Measurement of VH can therefore provide an indica-tion of the field B. This effect is exploited in Hall sensors. You will use onesuch sensor to measure B.

For the provided Hall effect sensor, the magnetic field (in Gauss) can beinferred from the voltage from the relationship,

B =(VH − 2.5)× 1000

k(1)

where VH is the output voltage (in volts) from the Hall sensor and k =3.123× 10−3 V/G. The Gauss is a unit of magnetic field and 1 G= 10−4 T.

3 The Experiment

Earth’s magnetic field can be resolved into two components, horizontal andvertical, Be = Bh + Bv. In this experiment we will measure only the

3

I

B

VH

Figure 2: The development of a Hall voltage (VH) through a sensor immersedin a magnetic field B through which a current I flows. The directions of thecurrent, field and Hall voltage are perpendicular.

.

horizontal component, Bh. The direction of Bh points towards the magneticnorth pole of the earth and a magnetic compass tends to align itself in thisdirection.

N

Bh

θ

(a) (b)

i

compass needle

Figure 3: Deflection of compass as a result of two magnetic fields (a) Showsour experimental configuration: the compass needle points in the NS direc-tion in the absence of current in the coil. (b) Shows the resultant of twomagnetic fields (Bcoil and Bh) when the current i has some non-zero value.The angle θ is the needle’s deflection from the original.

Measurement of the Bh will be done by the deflection galvanometer

4

method, sometimes also called tangent galvanometer method. In this methodan external magnetic field Bcoil is generated which makes angle of 90◦ withBh. This field, labelledBcoil, is produced by current flowing through a multi-turn coil whose axis is along the east-west direction. The overall orientationof the experiment is depicted in Figure 3 while a photograph of the variouscomponents is shown in Figure 4.

Figure 4: Experimental arrangement: (a) dc-power source (b) current con-troller switch (c) multi-turn coil connected to the power source (d) wooden-board with fitted rails (e) mounted Hall probe (f) magnetic compass (g)digital multimeter equipped with a voltmeter for measuring the Hall voltage.

The current through the coil is supplied from the dc power supply. Movethe compass to any desired distance on the coil axis and fix it at this distance.

5

Record the values of deflection of the compass against different values ofcurrent. Now at the same distance introduce a Hall probe and measure themagnetic field produced from the coil, for identical current values.

Q 2. From the data acquired, make appropriate tables, use the datato find the best estimate of the earth’s magnetic field (horizontal componentonly). What is your uncertainty in this measurement?

Q 3. Devise a method to find the effective radius of the multi-turn coilused in this experiment.

Q 4. How you can find the vertical component of the Earth’s magneticfield?

Q 5. A current-carrying wire is placed in the north-south orientation.What direction does the compass needle point when a compass needle isplaced below or above the wire?

6