doPhysics · Electromagnetism 2
Magnetism and Matter
The bar magnet as a magnetic dipole and its field. The Earth's magnetism, its declination, dip and horizontal component. Neutral points and the deflection and vibration magnetometers. The magnetisation of matter, dia-, para- and ferromagnetism, Curie's law and hysteresis.
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Why this chapter
Why this chapter exists
A current loop is a magnetic dipole, and so is every magnet. This chapter follows that idea outward and inward. Outward, to the bar magnet on the laboratory table and to the Earth itself, a magnet whose field steers every compass in India. Inward, to the atoms of matter. Their tiny current loops decide whether a material is pushed out of a field, drawn into it, or keeps a field of its own. On the way the chapter builds the deflection and vibration magnetometers of the Class 12 practical. With them it measures the Earth's field.
You will learn
By the end of this chapter you will
- Find the moment of a bar magnet from its poles, and its field on the axial and equatorial lines, with directions.
- Use the torque \(MB\sin\theta\) and energy \(-MB\cos\theta\) of a magnet, and explain a magnet as a set of current loops.
- State the three elements of the Earth's field, relate \(B_H\), \(B_V\) and the dip, and find an apparent dip.
- Locate neutral points, and use the tangent law in the tan A and tan B positions of a deflection magnetometer.
- Use \(T = 2\pi\sqrt{I/MB_H}\) to compare moments and fields, apply the sum and difference method, and find \(B_H\).
- Define magnetisation, intensity and susceptibility, sort materials into dia-, para- and ferromagnets, and use Curie's law and the hysteresis loop.
Before you begin
Before you begin
You need four results of the chapter Magnetic Force on Currents and the Magnetic Dipole. They are the moment \(M = NIA\), the torque \(\vec M \times \vec B\), the energy \(-\vec M \cdot \vec B\) and the period \(2\pi\sqrt{I/MB}\) of a swinging dipole. From Mechanics you need angular SHM. The chapter Sources of the Magnetic Field gives the field of a solenoid. The chapter Electric Flux and Gauss's Law gives the idea of flux.
Lessons
1
The Bar Magnet as a Dipole
A bar magnet has two equal poles and a magnetic moment \(M = m \times 2l\). On its axis its field is \(2M/r^3\) along \(M\); on its equatorial line it is \(M/r^3\) against \(M\). In a field it turns like a current loop, because inside it is a set of current loops.
Poles and the magnetic moment of a bar magnetField of a short magnet on its axis and equatorTorque and energy of a magnet in a fieldA magnet is a set of current loops
2
The Earth's Magnetic Field
The Earth behaves like a huge magnet tilted about 10° from its spin axis, with its south pole in the north. Three elements fix its field at a place: the declination, the dip and the horizontal component. A dip circle turned out of the meridian reads a larger, apparent dip.
The earth as a magnetDeclination dip and the horizontal componentApparent dipWhere the needle stands vertical
3
Neutral Points and the Deflection Magnetometer
Near a magnet on a table, its field adds to the Earth's horizontal field. Where the two cancel is a neutral point. Where they cross at right angles, a needle sets at \(\theta\) with \(\tan\theta = B/B_H\), which lets a deflection magnetometer compare a magnet with the Earth.
Neutral pointsThe deflection magnetometer tan a and tan bComparing two magnets by deflection
4
The Vibration Magnetometer
A magnet hung in the Earth's field swings about the meridian with \(T = 2\pi\sqrt{I/MB_H}\). Periods compare two moments, or two fields, and two magnets tied together give their ratio directly. With the deflection magnetometer, the period gives \(B_H\) itself.
A magnet oscillating in a fieldComparing moments by periodsThe sum and difference methodFinding the horizontal field
5
Magnetic Materials
A material in a field becomes magnetised. Its magnetisation per unit H is the susceptibility, which sorts materials into diamagnets, paramagnets and ferromagnets. A paramagnet weakens with heat by Curie's law, and a ferromagnet remembers its past along a hysteresis loop.
Magnetisation intensity and susceptibilityDia para and ferromagnetismCuries lawHysteresis retentivity and coercivity
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%The Workbook
Questions to solve on paper, marked by you.
Glossary
The key words of this chapter, with the meaning this chapter gives them.
- axial line
- The line through the two poles of a magnet. On it a short magnet's field is \((\mu_0/4\pi)\,2M/r^3\), along \(\vec M\).
- coercivity
- The reverse intensity \(H\) needed to bring the magnetic field in a ferromagnet back to zero.
- Curie temperature
- The temperature above which a ferromagnet loses its domains and becomes paramagnetic; \(1043\,\text{K}\) for iron.
- declination
- The angle between the magnetic meridian and the geographic meridian at a place, east or west.
- deflection magnetometer
- A compass needle in a box with a degree scale and two graduated arms. A magnet on an arm deflects the needle, and the tangent law gives \(M/B_H\).
- diamagnetic
- Having a small negative susceptibility, about \(-10^{-5}\). A diamagnet is pushed towards the weaker part of a field. Copper, water and bismuth are examples.
- dip
- The angle that the Earth's field makes with the horizontal at a place, measured in the magnetic meridian. It is also called the inclination.
- dip circle
- A magnetic needle pivoted on a horizontal axis, free to turn in a vertical plane, with a degree scale. Set in the magnetic meridian, it reads the dip.
- domains
- Small regions of a ferromagnet, up to about a millimetre across, in each of which all the atomic moments point the same way.
- elements of the Earth's field
- The three quantities that fix the Earth's field at a place: the declination, the dip and the horizontal component.
- equatorial line
- The line through the centre of a magnet, perpendicular to its axis. On it a short magnet's field is \((\mu_0/4\pi)\,M/r^3\), against \(\vec M\).
- ferromagnetic
- Having a very large positive susceptibility, because its atomic moments line up in domains. Iron, nickel and cobalt are examples.
- geographic meridian
- The vertical plane through a place and the geographic north and south poles.
- hysteresis
- The lagging of the magnetic field \(B\) in a ferromagnet behind the intensity \(H\), so that cycling \(H\) traces a closed loop.
- magnetic equator
- The line round the Earth on which the dip is zero and the Earth's field is horizontal.
- magnetic intensity
- The field \(\vec H = \vec B/\mu_0 - \vec M\), set by the free currents alone, in A/m. In a long solenoid \(H = nI\).
- magnetic length
- The distance \(2l\) between the two poles of a bar magnet, about five-sixths of its length measured with a ruler.
- magnetic meridian
- The vertical plane that contains a freely pivoted compass needle at rest, and so the Earth's field at that place.
- magnetisation
- The net magnetic moment per unit volume of a material, \(M\), in A/m.
- neutral point
- A point near a magnet where its field cancels the Earth's horizontal field, so that the total horizontal field is zero.
- null method
- A comparison of two magnets on opposite arms of a magnetometer, adjusted until their fields cancel at the needle and it shows no deflection.
- paramagnetic
- Having a small positive susceptibility, about \(10^{-5}\) to \(10^{-3}\). A paramagnet is drawn towards the stronger part of a field. Aluminium and oxygen are examples.
- pole strength
- The strength \(m\) of one pole of a magnet in the pole model, in A m. The two poles of a magnet have equal and opposite strengths.
- relative permeability
- The number \(\mu_r = 1 + \chi\) by which a material multiplies the field of the free currents, \(B = \mu_0\mu_r H\).
- retentivity
- The magnetic field that remains in a ferromagnet when the intensity \(H\) is brought back to zero. It is also called remanence.
- sum and difference method
- A comparison of two magnets tied together, swinging with their moments added and then opposed; \((M_1 + M_2)/(M_1 - M_2)\) \(= T_d^2/T_s^2\).
- susceptibility
- The ratio \(\chi = M/H\) of the magnetisation of a material to the magnetic intensity, a pure number.
- tan A position
- The layout of a deflection magnetometer with its arms along the magnetic east-west line, so that the needle lies on the magnet's axis.
- tan B position
- The layout of a deflection magnetometer with its arms along the magnetic meridian and the magnet across them. The needle then lies on the magnet's equatorial line.
- tangent law
- A needle in two perpendicular fields \(B\) and \(B_H\) rests at an angle \(\theta\) from \(B_H\) with \(B = B_H\tan\theta\).
- vibration magnetometer
- A magnet hung by an untwisted thread in a draught-free box. The period of its small swings, \(2\pi\sqrt{I/MB_H}\), gives \(MB_H\).