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Magnetism and matter are interconnected in a very interesting way.
- Magnetism is a physical property that develops due to a magnetic field, allowing objects to attract or repel each other.
- Magnetism is one of two characteristics of electromagnetism since both electric currents and magnetic moments of elementary particles produce a magnetic field.
- A magnet is a substance or object that produces a magnetic field.
- These days magnets have a lot of applications in areas such as electrical devices, motors, fans, power generation, etc.
- All magnets exhibit magnetic force around them which is represented in magnetic field lines.
- These lines start from the north pole of the magnet to the south pole.
- The earth itself exhibits magnetic field lines around making it act like a magnet.
Key terms: Gauss’s law, Magnetic field lines, Magnetic moment of the solenoid, Magnetic potential energy, Magnetization, Magnetic intensity, Gauss law, Ferromagnetic materials, Magnetic dipole, Magnet
Bar Magnet
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A substance that attracts small pieces of iron, steel, nickel, cobalt, etc., and rests in the North-South direction when suspended freely is called a magnet.
A bar magnet is generally a rectangular piece of magnet having south and north poles of equal strengths separated by a small distance.
A bar is also called a magnetic dipole.
Bar Magnet
Properties of Bar Magnet
The following are the properties of a bar magnet
- Poles of a magnet have the property to attract small pieces of magnetic materials.
- The strength with which a magnetic pole attracts is known as pole strength.
- The more pole strength more is the power.
- A magnet has the property of alignment.
- When suspended freely, magnets are aligned in the north-south direction.
- Like magnetic poles repel each other, while unlike magnetic poles attract each other.
- Magnetic poles always exist in pairs.
- Repulsion is the surest test for distinguishing between an iron piece and a magnet.
- Magnets have the property of induction.
Read more :
| Read More about Magnets | ||
|---|---|---|
| Magnetic Poles | Magnetic Declination | Magnetometer |
| Permanent Magnets and Electromagnets | Derivation of Biot Savart Law | Unit of Magnetic Field |
Coulomb's Law of Magnetic Force
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According to Coulom’s law of magnetic force, the force between two magnetic poles of strengths qm1 and qm2 lying at a distance r is directly proportional to the product of the pole strengths and inversely proportional to the square of the distance between their centers.
Mathematically
\(F_m=\frac {\mu_o}{4 \pi}\frac {q_{m1}q_{m2}}{r^2}\)
Where
- Fm is the magnetic force
- μo is the absolute permeability
- qm1 and qm2 are the pole strengths of the magnet
- r is the distance
Magnetic Field Lines
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All magnets exhibit a magnetic field around them. The magnetic field lines are the visual and intuitive realization of the magnetic field. Some of the properties of magnetic field lines are:
- Magnetic field lines form continuous closed loops.
- Tangent drawn at any point on the magnetic field line shows its direction.
- The larger the number of field lines per unit area, the stronger the magnetic field.
- They do not intersect each other.
- They run from the north to the south pole of the magnet.
The video below explains this:
Magnetic Properties of Substances value Detailed Video Explanation:
Magnetic Properties of Materials
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Substances can be divided into three groups based on their magnetic properties i.e. diamagnetic, paramagnetic, and ferromagnetic. They can be classified based on their magnetic susceptibility.
Diamagnetic Materials
- The materials that develop temporary magnetization in the opposite direction to that of the magnetic field in which they are placed are known as Diamagnetic materials.
- In simple words, they are repelled by magnets.
- Their magnetic susceptibility is small and negative.
- Examples of diamagnetic materials are Bismuth, Copper, Zinc, Lead, etc.
Diamagnetic Materials
Paramagnetic Materials
The materials that develop temporary magnetization in the same direction as that of the magnetic field in which they are placed are known as Paramagnetic materials.
- They are slightly attracted by magnets.
- They have positive but very low susceptibility.
- Examples of Paramagnetic materials are Aluminum, Sodium, Calcium, etc.
Paramagnetic Materials
Ferromagnetic Materials
The materials that develop temporary but strong magnetization in the opposite direction to that of the magnetic field in which they are placed are known as Ferromagnetic materials.
- They are strongly attracted by magnets.
- They have positive and high susceptibility.
- Examples of Ferromagnetic materials are Iron, Nickel, Cobalt, Haematite, etc.
Ferromagnetic Materials
Bar Magnet as an Equivalent Solenoid
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The magnetic field of a solenoid and a bar magnet can be practically found to be the same.
The magnetic field of a solenoid with radius a, carrying current I at distance r on the axis is given by the formula
\(B=\frac{\mu_0}{4 \pi} \frac{2m}{r^3}\)
Where
- m is the magnetic moment of the solenoid
- r is the distance from the solenoid to the point where the magnetic field is calculated
- B is the magnetic field
Bar Magnet as an Equivalent Solenoid
Dipole in a Uniform Magnetic Field
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Torque experienced by a magnetic dipole placed in a uniform magnetic field is given by
\(\tau=mB\ sin\theta\)
Where
- τ is the torque experienced by a magnetic dipole
- m is the magnetic moment
- B is the uniform magnetic field
- θ is the angle between m and B
The potential energy of a magnetic dipole placed in a uniform magnetic field is given by
\(U=-mB\ cos\theta\)
- When m and B are antiparallel, then the dipole has maximum potential energy and it is in unstable equilibrium i.e. U = mB
- When m and B are parallel, then the dipole has minimum potential energy and it is stable equilibrium i.e. U = -mB
Time period of the oscillation of a magnetic dipole executing simple harmonic motion placed in a uniform magnetic field is given by
\(T=2\pi \sqrt {\frac {I}{mB}}\)
Where I is the moment of inertia of the magnetic dipole.
Electric current and magnetism are interrelated to each other.
- No electric current can exist without producing magnetic fields.
- They both are complementary to each other, also they share lots of similarities due to this.
The analogy between the electric and magnetic dipoles is depicted in the table below, which will help you to understand and relate the theories better:
| Description | Electrostatics | Magnetism |
|---|---|---|
| Dipole moment | p | M |
| An equatorial field for a short dipole | \(\frac{-p}{4 \pi \epsilon_0 r^3}\) | \(\frac{- \mu_0 M}{4 \pi r^3}\) |
| An axial field for a short dipole | \(\frac{\mu_0 2M}{4 \pi r^3}\) | \(\frac{\mu_0 2M}{4 \pi r^3}\) |
| External field: torque | p . E | M . B |
| External field: energy | – p . E | – M . B |
Gauss’s Law for Magnetism
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Gauss’s law is one of the basic equations of electrodynamics.
- The surface through which the magnetic fields are passing is known as the Gaussian surface.
- Gauss’s law for electrodynamics states that the electric field passing through any close surface is the ratio of the charge “q” it encloses.
- Such a law can also be applied to magnetism.
- Unlike electrical charges, magnetic poles can not exist alone, they are always found in pairs. Thus it is almost impossible to have a unipolar magnet.
- Therefore, Gauss’s law for magnetism states that “The net magnetic flux through any closed surface is zero.
The net electric flux is given by
\(\phi_B=\sum \vec B.\Delta \vec s=\oint_s \vec B \times d \vec s=0\)
The net electric flux
Magnetization and Magnetic Intensity
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- Magnetization M of a sample is defined as the amount of net magnetic moment per unit volume.
- Magnetic intensity is a vector quantity.
- It is measured in the units of Am-1 with LM-1 as dimensions.
- Magnetization M can be written as: \(M = \frac{m_{net}}{V}\)
Important Formulas Related to Magnetic Intensity
Formulas related to magnetic intensity is given below.
| Description | Formula |
|---|---|
| The magnetic field in the interior of the solenoid | B0 = μ0 nI |
| The magnetic field inside the solenoid due to the magnetic core | Bm = μ0 m |
| Magnetic intensity | \(H = \frac{B}{\mu _0} - M\) |
| Magnetic field | B = μ0 (H + M) |
| Magnetic susceptibility | M = χ H |
| Relative Magnetic Permeability | μr = 1 + χ |
| The magnetic field in terms of 0 and r | B = μ0 μr H B = μ H |
Terms related to Magnetism
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Some of the important scientific terms related to the magnetism concept are given below.
- Gaussmeter: It is an instrument used to measure the intensity of an electromagnetic field in a given area. It is also known as the Tesla meter.
- Hysteresis: Hysteresis is a condition in which the material lags behind the changes in the alternating magnetic field. It is commonly observed in paramagnetic materials. It is also known as the Hysteresis loop.
- Remanence: Remanence or residual magnetism is the small amount of magnetism that remains in the material after it is exposed to a magnetic field.
- Coercive force: The amount of magnetic force required to nullify the residual magnetism or remanence of material is known as Coercive force.
- Curie temperature: It is the temperature at which the magnet starts losing its magnetic power
Basics Formulas of Magnetism
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The basic formulas in the Magnetism and Matter chapter are tabulated below:
| Description | Formula |
|---|---|
| The magnitude of the force between two magnetic poles (Coulomb's Law) | \(F = K \frac{\mu_0}{4 \pi} . \frac{m1m2}{r^2}\) |
| Magnetic Dipole Moment | M = m . 2l |
| Magnetic field due to bar magnet on axial point | \(B = \frac{\mu_0}{4 \pi} \frac{2M}{r^3}\) |
| Magnetic pole due to magnet on an equatorial point | \(B = \frac{\mu_0}{4 \pi} \frac{M}{r^3}\) |
Read more :
Things to Remember
- Magnetism is the force by which materials are attracted to a magnet.
- All magnets exhibit a magnetic field around it which is represented by means of magnetic field lines.
- The earth behaves like a magnet having magnetic field lines travelling from the north pole to the south pole.
- Based on the behavior in the presence and absence of a magnetic field, materials can be classified as paramagnetic, ferromagnetic, and diamagnetic.
- Magnetic properties have an electrostatic analog as well, e.g. coulomb’s law is an electrostatic analog of Biot savart law.
- Magnetization is the amount of net magnetic moment per unit volume.
Sample Questions
Ques. The permeability of a magnetic material is 0.9983. Name the type of magnetic materials it represents. (1 mark)
Ans. The above-mentioned material represents a diamagnetic substance.
Ques. The susceptibility of a magnetic material is 1.9 × 10-5. Name the type of magnetic materials it represents. (1 mark)
Ans. The above-mentioned material represents a paramagnetic substance.
Ques. Where on the surface of Earth is the angle of dip 90°? (1 mark)
Ans. The angle of dip is 90o at the magnetic poles on the surface of the Earth.
Ques. Where on the surface of Earth is the angle of dip zero? (1 mark)
Ans. The angle of dip is zero at the magnetic equator on the surface of the Earth.
Ques. Current flows through a circular loop. Depict the north and south poles of its equivalent magnetic dipole. (2 marks)
Ans. The direction of the magnetic field lines is given by the right-hand thumb rule.
Magnetic field lines
Ques. Why does material B, has a larger susceptibility than A, for a given field at constant temperature? (2 marks)
Ans. (b) Larger susceptibility is due to characteristic ‘domain structure’. More magnetic moments get aligned in the direction of the magnetizing field in comparison to that for paramagnetic materials for the same value of the magnetizing field.
(i) diamagnetic,
(ii) paramagnetic substance is placed in an external magnetic field.
Which magnetic property distinguishes this behavior of the field lines due to the two substances? (2 marks)
Ans. (i) When a diamagnetic material is placed in an external magnetic field.
Diamagnetic
ii) When a paramagnetic material is placed in an external magnetic field.
Paramagnetic
Magnetic susceptibility distinguishes this behaviour of the field lines due to the two substances.
Ques. A circular coil of N turns and radius R carries a current I. It is unwound and rewound to make another coil of radius R/2, current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. (3 marks)
Ans.
Ques. Write two properties of a material suitable for making
(a) a permanent magnet, and
(b) an electromagnet. (2 marks)
Ans. Properties of a material—
(a) For making a permanent magnet:
- High retentivity
- High coercivity
- High permeability
(b) For making an electromagnet:
- High permeability.
- Low retentivity
- Low coercivity
Ques. Define the following using suitable diagrams :
(i) magnetic declination and
(ii) angle of dip. In what direction will a compass needle point when kept at the
(i) poles and
(ii) equator? (3 marks)
Ans.
Magnetic declination: The angle between magnetic meridian and geographical meridian
Magnetic declination
The angle of dip: It is the angle that the magnetic needle makes with the horizontal in the magnetic meridian.
The angle of dip
- Direction of compass needle is vertical to the earth’s surface at poles.
- Parallel to the earth’s surface at equator.
Ques. The figure shows the variation of intensity of magnetisation versus the applied magnetic field intensity, H, for two magnetic materials A and B :
(a) Identify the materials A and B.
(b) Why does the material B, has a larger susceptibility than A, for a given field at constant temperature? (5 marks)
Ans. (a) As Xm = \(\frac{1}{H}\)
The slope of the line gives magnetic susceptibilities.
For magnetic material B, it is giving a higher +ve value.
Therefore, the material is ‘ferromagnetic’.
For magnetic material A, it is giving lesser +ve value than ‘B’.
Therefore, that material is ‘paramagnetic’.
(b) Larger susceptibility is due to characteristic ‘domain structure’. More number of magnetic moments get aligned in the direction of magnetising field in comparison to that for paramagnetic materials for the same value of the magnetizing field.
Ques. (a) A small compass needle of the magnetic moment ‘m’ is free to turn about an axis perpendicular to the direction of uniform magnetic field ‘B’. The moment of inertia of the needle about the axis is ‘I’. The needle is slightly disturbed from its stable position and then released. Prove that it executes simple harmonic motion. Hence deduce the expression for its time period.
(b) A compass needle, free to turn in a vertical plane orients itself with its axis vertical at a certain place on the earth. Find out the values of the horizontal component of the earth’s magnetic field and the angle of dip at the place. (5 marks)
Ans. a) This is done by placing a small compass needle of known magnetic moment m and moment of inertia I and allowing it to
(b) Since, the compass needle is oriented vertically
- Horizontal component of earth’s magnetic field will be zero.
- The value of angle of dip at that place will be 90°.
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