42Properties of Magnets

📚
MAGNETISM
▢ Properties of Magnets:

Table 1: Basic Properties

Fact
Answer
Natural magnet
Ore of iron: \(Fe_3O_4\)
Magnetic substances
Iron, steel, cobalt, nickel
Maximum attraction
At two ends of magnet
Ends of magnet
Magnetic poles
Freely suspended magnet
Rests along north-south direction
North pole
Pole pointing geographical north
South pole
Pole pointing geographical south
Poles
Always exist in pairs
Magnetic monopole
Does not exist
Like poles
Repel
Unlike poles
Attract
Sure test of magnetism
Repulsion
❖ Magnetic Meridian: Vertical plane passing through N-S line of freely suspended magnet
▢ Coulomb's Law of Magnetic Force:
❖ Statement: Force between two magnetic poles is directly proportional to product of pole strengths and inversely proportional to square of distance between their centres

Table 1: Magnetic Force Formulae

Quantity
Formula / Value
Proportionality
\(F\propto\frac{m_1m_2}{r^2}\)
General
\(F=K\frac{m_1m_2}{r^2}\)
SI constant
\(K=\frac{\mu_0}{4\pi}=10^{-7}\ WbA^{-1}m^{-1}\)
SI formula
\(F=\frac{\mu_0}{4\pi}\frac{m_1m_2}{r^2}\)
CGS constant
\(K=1\)
Pole strength unit
Ampere-metre \((Am)\)
▢ Atomic or Molecular Theory of Magnetism:
❖ Postulates:
  1. Every molecule of magnetic substance is a complete magnet with equal north and south pole
  2. In unmagnetised substance, molecular magnets are randomly oriented and form closed chains
  3. Random orientation makes resultant magnetism zero
  4. On magnetisation, molecular magnets align in same direction
  5. When all molecular magnets are fully aligned, substance is saturated with magnetism
  6. At every stage, strengths of two poles developed are equal
  7. On heating, molecular magnets gain kinetic energy and may return to closed-chain arrangement
  8. Heating reduces magnetism
▢ Magnetic Field and Lines of Force:

Table 1: Magnetic Field Units

Quantity
Value
SI unit of magnetic field strength
Tesla \((T)\)
1 Tesla
\(1\ NA^{-1}m^{-1}=1\ Wbm^{-2}\)
CGS unit
Gauss \((G)\)
1 Gauss
\(10^{-4}\ T\)
❖ Magnetic Lines of Force:
  • •
    Continuous closed curves
  • •
    Outside magnet: north pole to south pole
  • •
    Inside magnet: south pole to north pole
  • •
    Electric lines of force are discontinuous, magnetic lines are continuous
  • •
    Tangent at any point gives direction of magnetic field
  • •
    No two magnetic lines intersect
  • •
    Magnetic lines contract longitudinally
  • •
    Magnetic lines dilate laterally
  • •
    Crowding of lines indicates stronger magnetic field
▢ Magnetic Dipole:
❖ Definition: Two unlike poles of equal pole strength separated by small distance

Table 1: Magnetic Dipole Moment

Quantity
Formula / Meaning
Magnetic dipole moment
\(\vec M=m\times2\vec l\)
Magnitude
\(M=m(2l)\)
Direction
From south pole to north pole
Geometrical length
\(2l\)
Magnetic length
\(0.85\times2l\)
Current loop magnetic moment
\(\vec M=IA\hat n\)
❖ Dipole Moment Combination:

Table 1: Resultant Magnetic Moment

Arrangement
Resultant
Two magnets inclined at angle \(\theta\), like poles together
\(M=\sqrt{M_1^2+M_2^2+2M_1M_2\cos\theta}\)
Two magnets at \(90^\circ\)
\(M=\sqrt{M_1^2+M_2^2}\)
Like poles together, \(\theta=0^\circ\)
\(M=M_1+M_2\)
Unlike poles together, \(\theta=180^\circ\)
\(M=M_1-M_2\)
Inclined at angle \(\theta\), unlike poles together
\(M=\sqrt{M_1^2+M_2^2-2M_1M_2\cos\theta}\)
❖ Gauss Theorem in Magnetism:
◉ Statement: Surface integral of magnetic field over a closed surface is zero
◉ Formula: \(\oint \vec B\cdot d\vec A=0\)
◉ Conclusion: Magnetic poles always exist in equal and unlike pairs
❖ Bent Magnet:

Table 1: Bent Magnet Formulae

Condition
Result
Bar magnet length \(2l\), moment \(M\), bent at middle by angle \(\theta\)
New length \(2l'=2l\sin\frac{\theta}{2}\)
New dipole moment
\(M'=M\sin\frac{\theta}{2}\)
Magnetized wire bent into arc subtending angle \(\theta\)
\(M'=M\frac{2\sin(\theta/2)}{\theta}\), \(\theta\) in radian
▢ Magnetic Field Due to Dipole:

Table 1: General Dipole Field and Potential

Quantity
Formula
Magnetic field
\(B=\frac{\mu_0}{4\pi}\frac{M\sqrt{1+3\cos^2\theta}}{r^3}\)
Field proportionality
\(B\propto\frac{1}{r^3}\)
Magnetic potential
\(V=\frac{\mu_0}{4\pi}\frac{M\cos\theta}{r^2}\)
Potential proportionality
\(V\propto\frac{1}{r^2}\)

Table 2: Axial and Equatorial Positions

Position
Field
Short dipole field
Potential
Direction
Axial / end-on / tan A
\(B_a=\frac{\mu_0}{4\pi}\frac{2Mr}{(r^2-l^2)^2}\)
\(B_a=\frac{\mu_0}{4\pi}\frac{2M}{r^3}\)
\(V=\frac{\mu_0}{4\pi}\frac{M}{r^2}\)
Along \(\vec M\)
Equatorial / broadside-on / tan B
\(B_e=\frac{\mu_0}{4\pi}\frac{M}{(r^2+l^2)^{3/2}}\)
\(B_e=\frac{\mu_0}{4\pi}\frac{M}{r^3}\)
\(V=0\)
Opposite to \(\vec M\)
❖ Ratio: \(B_a:B_e=2:1\)
❖ Do You Know:
  • •
    At axial line, magnetic field is along magnetic moment
  • •
    At equatorial line, magnetic field is opposite to magnetic moment
▢ Force Between Magnetic Dipoles:
❖ **table:
    ▢ Magnetic Dipole in Uniform Magnetic Field:
    ❖ Condition: Dipole moment \(\vec M\) kept in uniform magnetic field \(\vec B\)
    ❖ **table:
      ◈ caption: Special Positions
      ◈ data:
        1. Angle
        2. Net force
        3. Torque
        4. Potential energy
        5. Equilibrium
        1. \(0^\circ\)
        2. 0
        3. 0 minimum
        4. \(-MB\) minimum
        5. Stable
        1. \(90^\circ\)
        2. 0
        3. \(MB\) maximum
        4. 0
        5. —
        1. \(180^\circ\)
        2. 0
        3. 0 minimum
        4. \(+MB\) maximum
        5. Unstable
    ❖ Variation:
    • •
      As \(\theta\) increases from 0° to 180°, torque first increases, becomes maximum at 90°, then decreases to zero
    • •
      Potential energy keeps increasing up to 180°
    • •
      If initial angle is not given, assume \(\theta_1=0^\circ\)
    ▢ Neutral Points:
    ❖ Definition: Points where net magnetic field due to bar magnet and horizontal component of earth's field becomes zero

    Table 1: Position of Neutral Points

    Magnet position
    Neutral point position
    Condition
    N-pole towards geographic north
    Equatorial / broadside-on line
    \(B_e=H\)
    N-pole towards geographic south
    Axial line
    \(B_a=H\)
    ❖ Important Point: At neutral point, resultant magnetic field is zero
    ▢ Bohr Magneton:
    ❖ Concept: Revolving electron behaves as current loop and produces magnetic dipole moment
    ❖ Current Direction: Electron anticlockwise motion gives clockwise conventional current
    ❖ Pole Formation: Upper face acts as south pole and lower face acts as north pole

    Table 1: Bohr Magneton

    Quantity
    Formula / Meaning
    Magnetic moment of electron in orbit
    \(M=IA\)
    Bohr magneton
    \(\mu_B=\frac{eh}{4\pi m}\)
    Magnetic moment in nth orbit
    \(M=n\mu_B\)
    Principal quantum number
    \(n=1,2,3,...\)
    Definition
    Magnetic dipole moment due to orbital motion of electron in first orbit of hydrogen atom
    ▢ Magnetic Materials Properties:

    Table 1: Magnetic Quantities

    Quantity
    Symbol
    Meaning
    Unit
    Magnetising field
    \(\vec H\)
    Field in which material is placed for magnetisation
    \(A/m\)
    Intensity of magnetisation
    \(\vec I\)
    Induced magnetic dipole moment per unit volume
    \(A/m\)
    Magnetic susceptibility
    \(\chi_m\)
    \(\chi_m=\frac{I}{H}\); ease of magnetisation
    No unit, no dimension
    Magnetic permeability
    \(\mu\)
    \(\mu=\frac{B}{H}\); penetration of field lines in material
    \(H/m\)
    Relative permeability
    \(\mu_r\)
    \(\mu_r=\frac{\mu}{\mu_0}\)
    No unit, no dimension
    ❖ Permeability and Susceptibility:
    ◉ Relation: \(\mu_r=1+\chi_m\)
    ◉ Vacuum: \(\chi_m=0,\ \mu_r=1\)
    ◉ Air at STP: \(\chi_m\approx0.04,\ \mu_r\approx1.04\)
    ◉ Magnetic Field in Material: \(\vec B=\vec B_0+\vec B_I\)
    ▢ Earth's Magnetic Field:

    Table 1: Earth's Magnetism

    Fact
    Answer
    Earth model
    Giant fictitious bar magnet inside earth
    Magnetic north pole of earth's magnet
    Towards geographic south
    Magnetic south pole of earth's magnet
    Towards geographic north
    Earth field nature
    Approximately giant magnetic dipole
    Magnetic axis
    Inclined roughly 20° west of earth's rotational axis
    Field strength order
    \(10^{-4}\ T\)
    Magnetic poles
    Points where axis of fictitious magnet cuts earth's surface
    Near geographic north
    South magnetic pole
    Near geographic south
    North magnetic pole
    Direction of horizontal component above earth
    Geographic south to geographic north
    ▢ Magnetic Elements of Earth:
    ❖ Magnetic Meridian: Vertical plane passing through magnetic north and south of freely suspended magnet
    ❖ Geographical Meridian: Vertical plane passing through geographic north and south poles at a place
    ❖ Declination:
    ◉ Symbol: \(\theta\)
    ◉ Definition: Angle between magnetic meridian and geographical meridian

    Table 1: Declination

    Point
    Answer
    Determined by
    Kew magnetometer
    At equator
    About \(17^\circ\)
    Nature
    Varies from place to place
    Isogonal / isogonic lines
    Lines joining places of equal declination
    Agonal / agonic lines
    Lines joining places of zero declination
    ❖ Dip or Inclination:
    ◉ Symbol: \(\delta\)
    ◉ Definition: Angle made by total intensity of earth's magnetic field with horizontal line in magnetic meridian

    Table 1: Angle of Dip

    Point
    Answer
    Instrument
    Dip circle
    Range
    \(0^\circ\) to \(90^\circ\)
    At magnetic equator
    \(0^\circ\)
    At poles
    \(90^\circ\)
    Isoclinal / isoclinic lines
    Lines joining places of equal dip
    Aclinal / aclinic lines
    Lines joining places of zero dip
    ❖ Horizontal and Vertical Components:

    Table 1: Earth Field Components

    Quantity
    Formula / Result
    Horizontal component
    \(H=R\cos\delta\)
    Vertical component
    \(V=R\sin\delta\)
    Total intensity
    \(R^2=H^2+V^2\)
    Dip relation
    \(\tan\delta=\frac{V}{H}\)
    At poles
    \(\delta=90^\circ,\ V=R,\ H=0\)
    At equator
    \(\delta=0^\circ,\ H=R,\ V=0\)
    Equal horizontal component lines
    Isodynamical lines
    ◉ Arbitrary Vertical Plane:
    ◈ Formulae:
    • •
      \(H'=H\cos\theta\)
    • •
      \(V'=V\)
    • •
      \(\tan\delta'=\frac{V}{H'}\)
    ◈ Conclusion: Dip increases in a plane inclined to magnetic meridian; for \(\theta=90^\circ\), dip needle stands vertical
    ◉ Magnetic Latitude:
    ◈ Relation: \(\tan\delta=2\tan\lambda\)
    ◈ Small Angle: \(\delta=2\lambda\)
    ▢ Classification of Magnetic Materials:

    Table 1: Paramagnetic vs Diamagnetic vs Ferromagnetic

    Feature
    Paramagnetic
    Diamagnetic
    Ferromagnetic
    Magnetic field response
    Attracted weakly
    Repelled weakly
    Attracted strongly
    Orientation in field
    Same direction as applied field
    Opposite direction to applied field
    Same direction as applied field
    Susceptibility
    Small positive
    Small negative
    Large positive
    Relative permeability
    Slightly greater than 1
    Slightly less than 1
    Much greater than 1
    Examples
    Oxygen, aluminium, tin
    Hydrogen, beryllium
    Iron, cobalt, nickel
    Temperature effect
    Decreases with temperature
    Nearly temperature independent
    Becomes paramagnetic above Curie temperature
    ❖ Extra Points:
    • •
      Diamagnetism is universal property of all substances
    • •
      Superconductors show perfect diamagnetism
    • •
      Origin of diamagnetism: orbital motion of electrons
    • •
      Origin of paramagnetism and ferromagnetism: spin magnetic moment of electrons
    • •
      Paramagnets get magnetized by orientation of atomic magnetic moments
    • •
      Ferromagnets get magnetized by increase of domain area along field
    • •
      Domain formation is necessary feature of ferromagnetism
    • •
      At Curie temperature, ferromagnets become paramagnetic
    • •
      At Neel temperature, antiferromagnets become paramagnetic
    • •
      H-atom is paramagnetic; hydrogen molecule is diamagnetic
    • •
      Magnetic moment of noble gases is zero
    ▢ Magnetic Hysteresis:
    ❖ Definition: Lagging of magnetic induction \(B\) behind magnetising field \(H\) in ferromagnetic materials
    ❖ Occurs In: Only ferromagnetic materials
    ❖ Cause: After removing external field, magnetic moments of some domains remain aligned causing residual magnetism

    Table 1: Hysteresis Terms

    Term
    Meaning
    Retentivity / remanence
    Residual magnetism left when magnetising field is removed
    \(OC\)
    Residual magnetism \(B_r\)
    Coercivity
    Reverse magnetising field required to destroy residual magnetism
    \(OD\)
    Coercive field \(H_C\)
    Hysteresis loss
    Energy loss per cycle, proportional to area of loop
    ▢ Soft Iron and Steel Hysteresis Loops:

    Table 1: Soft Iron vs Steel

    Feature
    Soft iron
    Steel
    Loop
    Tall and narrow
    Tall and wide
    Coercivity
    Low
    High
    Retentivity
    High
    High / suitable for permanent magnet
    Hysteresis loss
    Less
    More
    Susceptibility
    High
    Less
    Permeability
    High
    Less
    Uses
    Transformers, moving coil galvanometers, electromagnets
    Permanent magnets
    ❖ Important Notes:
    • •
      Electromagnets are made of soft iron due to high permeability and low coercivity
    • •
      Permanent magnets should have high retentivity and high coercivity
    • •
      Adding 4% silicon to soft iron makes it ideal for electromagnets
    • •
      Narrowest hysteresis loop is for permalloy
    • •
      Ferrites have low conductivity
    ▢ Tangent Law:
    ❖ Statement: When a magnet is under two uniform magnetic fields \(F\) and \(H\) at right angles, it rests making angle \(\theta\) with \(H\)
    ❖ Formula: \(F=H\tan\theta\)
    ❖ Application: Tangent galvanometer is based on tangent law
    ▢ Deflection Magnetometer:
    ❖ Use: Compares magnetic moments of two magnets and measures horizontal component
    ❖ Principle: Tangent law
    ❖ Most Sensitive: Deflection \(0^\circ\)
    ❖ Most Accurate: Deflection nearly \(45^\circ\)
    ❖ End-On Position:
    ◉ Also Called: Tangent A position
    ◉ Arrangement: Arms along east-west; magnet length parallel to arms
    ◉ Formula: \(F=H\tan\theta\)
    ◉ For Short Magnet: \(B_a=\frac{\mu_0}{4\pi}\frac{2M}{d^3}\)
    ❖ Broadside-On Position:
    ◉ Also Called: Tangent B position
    ◉ Arrangement: Arms along north-south; magnet length perpendicular to arms
    ◉ Formula: \(F=H\tan\theta\)
    ◉ For Short Magnet: \(B_b=\frac{\mu_0}{4\pi}\frac{M}{d^3}\)
    ▢ Vibration Magnetometer:
    ❖ Use:
    • •
      Compares horizontal components of earth's magnetic field at two places
    • •
      Compares magnetic moments of two magnets
    • •
      Determines magnetic moment of a magnet

    Table 1: Vibration Magnetometer Formulae

    Quantity
    Formula / Meaning
    Time period
    \(T=2\pi\sqrt{\frac{I}{MH}}\)
    \(I\)
    Moment of inertia of magnet
    \(H\)
    Horizontal component of earth's field
    \(M\)
    Magnetic moment
    Magnetic moment
    \(M=\frac{4\pi^2I}{T^2H}\)
    Same magnet at two places
    \(\frac{H_1}{H_2}=\frac{T_2^2}{T_1^2}\)
    Two magnets of same size and mass
    \(\frac{M_1}{M_2}=\frac{T_2^2}{T_1^2}\)
    ❖ Combination of Two Magnets:

    Table 1: Like and Unlike Poles Together

    Arrangement
    Moment of inertia
    Magnetic moment
    Time period
    Like poles together
    \(I_1+I_2\)
    \(M_1+M_2\)
    \(T_1\)
    Unlike poles together
    \(I_1+I_2\)
    \(M_1-M_2\)
    \(T_2\)
    ◉ Important Point: Time period is greater when unlike poles are together than when like poles are together
    ▢ Rest and Digest:
    ❖ _*table:
      ▢ High-Yield Recall:

      Table 1: Magnetism One-Liners

      Fact
      Answer
      Natural magnet
      \(Fe_3O_4\)
      Magnetic monopole
      Does not exist
      Sure test of magnetism
      Repulsion
      Magnetic force
      \(F=\frac{\mu_0}{4\pi}\frac{m_1m_2}{r^2}\)
      Pole strength unit
      Ampere-metre
      Magnetic field SI unit
      Tesla
      1 gauss
      \(10^{-4}T\)
      Magnetic lines
      Continuous closed curves
      Magnetic dipole moment
      \(M=m(2l)\)
      Direction of \(M\)
      South to north
      Current loop moment
      \(M=IA\)
      Magnetic length
      \(0.85\times\) geometrical length
      Short dipole axial field
      \(B_a=\frac{\mu_0}{4\pi}\frac{2M}{r^3}\)
      Short dipole equatorial field
      \(B_e=\frac{\mu_0}{4\pi}\frac{M}{r^3}\)
      Dipole field ratio
      \(B_a:B_e=2:1\)
      Torque on magnetic dipole
      \(\tau=MB\sin\theta\)
      PE of magnetic dipole
      \(U=-MB\cos\theta\)
      Stable equilibrium
      \(\theta=0^\circ\)
      Unstable equilibrium
      \(\theta=180^\circ\)
      Bohr magneton
      \(\mu_B=\frac{eh}{4\pi m}\)
      Hydrogen atom magnetic moment
      \(\mu_B\)
      Susceptibility
      \(\chi_m=\frac{I}{H}\)
      Relative permeability
      \(\mu_r=\frac{\mu}{\mu_0}\)
      Relation
      \(\mu_r=1+\chi_m\)
      Earth magnetic field order
      \(10^{-4}T\)
      Declination
      Angle between magnetic and geographical meridian
      Dip
      Angle made by earth field with horizontal
      Horizontal component
      \(H=R\cos\delta\)
      Vertical component
      \(V=R\sin\delta\)
      Dip relation
      \(\tan\delta=\frac{V}{H}\)
      Magnetic latitude relation
      \(\tan\delta=2\tan\lambda\)
      Paramagnetic
      \(\chi>0,\ \mu_r>1\)
      Diamagnetic
      \(\chi<0,\ \mu_r<1\)
      Ferromagnetic
      \(\chi\) large positive
      Hysteresis
      Lagging of \(B\) behind \(H\)
      Retentivity
      Residual magnetism
      Coercivity
      Reverse field to remove residual magnetism
      Soft iron
      Electromagnets, transformers
      Steel
      Permanent magnets
      Tangent law
      \(F=H\tan\theta\)
      Vibration magnetometer
      \(T=2\pi\sqrt{\frac{I}{MH}}\)
      Q1.
      Angle of dip where earth's magnetic field is vertical is: [BP 2014]
      Q2.
      The magnetic susceptibility is negative for [BP 2013,12]
      Q3.
      ' Magnetic moment of a magnet decreases by 19%, then time period:
      Q4.
      The value of Bohr magneton is [BP 2013]
      Q5.
      Permanent magnets are made up of [BP 2010]
      Q6.
      When a magnet is heated, its magnetic moment is [BP 2010]
      Q7.
      A magnetic needle is kept in a non-uniform magnetic field. It experience [MOE 2014]
      Q8.
      A magnetic material aligns perpendicular to uniform magnetic field then the substance is: [MOE 2014]
      Q9.
      Susceptibility above Curie's temperature is valid for: [MOE 2010]
      Q10.
      A unit magnetic pole placed at a point on the perpendicular bisector line of a bar magnet placed in magnetic meridian experiences a force due to the magnet. The direction of the force experienced by it will be: [MOE 2011]
      Q11.
      When 2 A current is passed through tangent galvanometer, it gives a deflection of 30°. For deflection of 60°, the current must be. [MOE 2013]
      Q12.
      A compass needle is allowed to move horizontal plane is taken to a geomagnetic pole. It [KU 2012]
      Q13.
      The substance which when placed in external magnetic field are feebly magnetized in opposite direction to that of the magnetizing field are: [KU 2011]
      Q14.
      Magnetic meridian is- [IE 2013]
      Q15.
      S.I unit equivalent to the magnetic field Tesla (T) may be [MOE 09]
      Q16.
      The value of magnetizing field (H) when magnetic flux density (B) = 0 is called [Bangladesh 09]
      Q17.
      At a place the vertical and horizontal component of earth's magnetic field are equal. The angle of dip at that place is [KU 08]
      Q18.
      Area of hysteresis curve indicates. [KU 08]
      Q19.
      Soft iron is a suitable material for the core of transformer because it has
      Q20.
      The apparent angles of dip at two meridians perpendicular to each other about magnetic meridian are 45° and 45°. Then cot of the true angle of dip at that place is [BPKIHS 02]
      Q21.
      The magnetic field strength at a distance d from a short bar magnet in longitudinal to transverse position are in the ratio of: [BPKIHS 05]
      Q22.
      Above curie temperature ? [BP 2006/2016]
      Q23.
      The time period of magnet is 2 sec. It is cut into two equal parts by cutting it parallel to its length. What is the new time period of each part when vibrated in the same magnetic field? [BPKIHS-06]
      Q24.
      Why are laminated core placed in transformer? [BPKIHS-97]
      Q25.
      Which of the following is used in the core of an electromagnet [BPKIHS 1999]
      Q26.
      When the temperature increase, magnetic moment of a magnet [BPKIHS 1999]
      Q27.
      Null point is observe at the equatorial line of a bar magnet then the north pole of bar magnet must have faced [IE-03]
      Q28.
      If a magnetic material moves from stronger to weaker parts of a magnetic field, then it is
      Q29.
      When a thin bar magnet is cut in length into two equal halves and joined one above another facing same pole together the final time period of magnet is equal to: (if initial time period of magnet =T) [IOM 03]
      Q30.
      The ratio of the magnetic moment of two short magnets, which give null deflection in tan B position at 12cm and 18 cm from the centre of a deflection magnetometer is [MOE 2000]
      Q31.
      What is the net magnetic moment of two identical magnets each of magnetic moment Mo, inclined at 60° with each other?
      Q32.
      A thin bar magnet of length 2L and magnetic moment M is bent at mid-point so that the angle between them is 60°. The new magnetic moment is
      Q33.
      A magnetized steel wire having dipole moment M is bent at 30° at mid-point. Find the dipole moment of new wire.
      Q34.
      The ratio of magnetic fields due to a small bar magnet at a given distance in the end on position to broad side on position is
      Q35.
      A bar magnet is cut into two equal halves by a plane parallel to the magnetic axis. Of the following physical quantities, the one which remains unchanged is .
      Q36.
      The points A and B are situated perpendicular to the axis of 2cm long bar magnet at large distances x and 3x from the centre on opposite sides. The ratio of magnetic fields at A and B will be approximately equal to
      Q37.
      Two points A and B are situated at a distance x and 2x respectively from the nearer pole of magnet 2cm long. The ratio of magnetic field at A and B is
      Q38.
      The ratio of magnetic potentials due to magnetic dipole in the end on position to that in broad on position for the same distance from it is
      Q39.
      The magnetic potential at a point distant 10cm from the middle point of a magnetic dipole on a line inclined at an angle of 60° with the axis is 3 e.m.u. Then the magnetic moment of magnet is
      Q40.
      The magnet of pole strength m and magnetic moment M is cut into two pieces along its axis. Its pole strength and magnetic moment now become
      Q41.
      A large magnet is broken into two pieces so that their lengths are in the ratio 2:1. The pole strengths of the two pieces will have ratio
      Q42.
      A magnetic dipole is placed at right angles to the direction of lines of for magnetic induction B. If it is rotated through an angle of 180°, then the work done is
      Q43.
      Calculate force exerted on a point N pole of a 3200A-m placed 10cm away from a point south pole of 40A-m in air
      Q44.
      Two magnets of equal magnetic moment M each are placed as shown in figure. The resultant magnetic moment is
      Q45.
      A bar magnet is held at right angle to a uniform magnetic field. The couple acting on a magnet is to be halved by rotating it from this position. The angle of rotation is
      Q46.
      Torques τ1, and τ2 are required for a magnetic needle to remain perpendicular to the magnetic fields B1 and B2 at two different places. The ratio is B1/B2 is
      Q47.
      The distance between the poles of a horse shoe magnet is 4cm. The pole strength of each pole is 40 units. The magnetic potential midway between the poles is
      Q48.
      The force between two short bar magnets with magnetic moments M1 and M2 whose centres are r metre apart is 8N, when their axes are in the same line. If the separation is increased to 2r, the force between them is reduced to
      Q49.
      A magnetic needle lying parallel to a magnetic field required W units of work to turn it through 60°. The torque required to maintain the needle in this position is
      Q50.
      A thin magnet is cut into two equal parts by cutting it parallel to its length. If the original time period of vibration is 4sec, the time period of each part in the same field will be
      Q51.
      At a certain place, horizontal component is √3 times the vertical component. The angle of dip at this place is
      Q52.
      Two bar magnets of the same mass, same length and breadth but having magnetic moments M and 2M are joined together pole for pole and suspended by a string. The time period of assembly in a magnetic field of strength H is 30 seconds. If now the polarity of one of the magnets is reversed and the combination is again made to oscillate in the same field, the time of oscillation is
      Q53.
      In end on and broadside on position of deflection magnetometer, if θ_1 and θ_2 are the deflections produced by short magnets at equal distances, then tan⁡θ_1 /tan⁡θ_2 is
      Q54.
      At a place of latitude 5°, the angle of dip is nearly
      Q55.
      Two short magnets have equal pole strengths but one is twice as long as the other. The shorter magnet is placed 20cm in tan A position from the compass needle. The longer magnet must be placed on the other side of the magnetometer for no deflection at a distance equal to
      Q56.
      A magnetic dipole is placed in two perpendicular magnetic field B ⃗ and H ⃗ and is in equilibrium making angle θ with B ⃗ Then,
      Q57.
      A circular coil of radius 20cm and 20 turns of wire is mounted vertically with its plane in magnetic meridian. A small magnetic needle is placed at the centre of the coil and is deflected through 45° when a current is passed through the coil. When horizontal component of earth's field is 0.34×10^-4 T, the current in the coil is
      Q58.
      When 2A current is passed through a tangent galvanometer, it gives a deflection of 30°. For deflection of 60°, the current must be
      Q59.
      Horizontal component of earth's field at a height of 1m from the surface of earth is H. Its value at a height of 10m from the surface of earth is
      Q60.
      A superconductor exhibits perfect
      Q61.
      For a diamagnetic material
      Q62.
      The moment of magnet (15cm×2cm×1cm) is 1.2 A-m2. What is its intensity of magnetization?
      Q63.
      The core of an electromagnet is made of soft iron, because
      Q64.
      The hysteresis cycle for the material of permanent magnet is
      Q65.
      A magnetizing field of 2×103 amp/m produces a magnetic flux density of 8π tesla in a rod. The relative permeability of the rod will be
      Q66.
      Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together. 12 oscillations per minute are made but for unlike poles together only 4 oscillations per minute are executed. The ratio of their magnetic moments is
      Q67.
      When a thin bar magnet is cut in length into equal halves and joined one above the other facing same pole together, the final time period of the magnet is equal to (if the initial time period =T)
      Q68.
      A magnet of magnetic moment M is revolved end for end in a uniform magnetic field B. The change in kinetic energy of the magnet will be
      Q69.
      A magnet of length 2l is bent at mid at 60°. Find the new length of the magnet
      Q70.
      If a magnet is revolved end for end in a uniform magnetic field, the kinetic energy of magnet
      Q71.
      Material A is used as a permanent magnet. It means [MOE Curriculum]
      Q72.
      Which of the following is paramagnetic? [IOM 2015]