A magnetic dipole is oscillating in a magnetic field obeying the following expression d 2 θ dt 2 = - mB I θ : What is the time period of oscillation and mention the nature of oscillation?

Given The equation of oscillation is, d 2 θ dt 2 = - mB I θ , Where, m = magnetic moment. I =moment of inertia. B = magnetic field intensity. θ = the angle of the oscillating dipole at time t . Hence, the angular velocity is dθ dt and the angular acceleration is d 2 θ dt 2 As given the angular acceleration d 2 θ dt 2 = - mB I θ . Comparing this with the equation of angular oscillation ω 2 = MB I or ω = MB I This shows that the angular acceleration is proportional to the angular displacement and minus sign indicates that it is directed towards the mean position. Hence, the oscillation is angular simple harmonic motion. The time period of an angular SHM is given by T = 2 π ω so T = 2 π I MB . Hence the time period of the dipole is T = 2 π I M B and the oscillations are the angular SHM.

Of two metals A and B, it is found that χ A > > 1 and - 1 ≤ χ B < 0 . Name the types of materials to which the metals A and B do belong. Give one example of each.

Magnetic susceptibility is a measure of how a magnetic material responds to an external magnetic field. For material A, the susceptibility, χ A > > 1 hence, is a ferromagnetic material. The susceptibility of material B lies between - 1 and 0 hence, it is a diamagnetic material. Copper is a diamagnetic material and iron is an example of ferromagnetic material.

Of two metals A and B, it is found that χ A > > 1 and - 1 ≤ χ B < 0 . Name the types of materials to which the metals A and B do belong. Give one example of each.

Magnetic susceptibility is a measure of how a magnetic material responds to an external magnetic field. For material A, the susceptibility, χ A > > 1 hence, is a ferromagnetic material. The susceptibility of material B lies between - 1 and 0 hence, it is a diamagnetic material. Copper is a diamagnetic material and iron is an example of ferromagnetic material.

A magnetic dipole is oscillating in a magnetic field obeying the following expression d 2 θ dt 2 = - mB I θ : What is the time period of oscillation and mention the nature of oscillation?

Given The equation of oscillation is, d 2 θ dt 2 = - mB I θ , Where, m = magnetic moment. I =moment of inertia. B = magnetic field intensity. θ = the angle of the oscillating dipole at time t . Hence, the angular velocity is dθ dt and the angular acceleration is d 2 θ dt 2 As given the angular acceleration d 2 θ dt 2 = - mB I θ . Comparing this with the equation of angular oscillation ω 2 = MB I or ω = MB I This shows that the angular acceleration is proportional to the angular displacement and minus sign indicates that it is directed towards the mean position. Hence, the oscillation is angular simple harmonic motion. The time period of an angular SHM is given by T = 2 π ω so T = 2 π I MB . Hence the time period of the dipole is T = 2 π I M B and the oscillations are the angular SHM.

Define magnetisation and magnetic intensity. Deduce the relation among relative magnetic permeability, permeability of vacuum and magnetic susceptibility. What is the values of susceptibility of a superconductor?

Magnetisation: Magnetization is the process that makes a substance magnetic (temporarily or permanently)magnetisation is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Diametric Magnetic intensity: The ability of a magnetic field to magnetize a material medium is called its magnetic intensity H . Its magnitude is measured by the number of ampere-turns flowing round unit length of a solenoid, required to produce that magnetic field.Unit of H is ampere-turns per meter Am - 1 . Dimension M 0 L - 1 T 0 A H = net magnetic moment volume = m × 2 l a × 2 l = m a , where m = magnetic pole strength, a = area of cross section and 2 l = length of the magnet. Relation between magnetic susceptibility and magnetic permeability: When we place a magnetic material in a magnetic field of magnetic intensity H , the material gets magnetised. The total magnetic field B is the sum of the magnetic field in a vacuum B 0 and the magnetic field due to magnetisation B m . Hence , B = B 0 + B m since B 0 = μH and B m = μ 0 I ,where μ 0 = permeability of free space. Therefore, we have, B = μ 0 H + I m . As magnetic susceptibility is given by Χ = I m H or I m = ΧH , so we get, B = μ 0 H + ΧH = μ 0 H 1 + ΧH . Also B = μH , so we can write μ H = μ 0 H 1 + ΧH , where μ = permeability of the medium. Therefore, we get for relative permeability, μ r = μ μ 0 = ( 1 + Χ ) . This is the required relation. The susceptibility of superconductor is - 1 , as they are perfect diamagnetic substances

Define the elements of the earth's magnetic field.

The elements of the earth's magnetic field are: (1) Magnetic Inclination: This angle is the angle made with the horizontal by the compass needle of a vertically held compass. This angle varies at different points on the Earth's surface. At the equator, the magnetic field is parallel to the horizon, so there will be zero angle of dip. At poles the magnetic field is almost vertical, here the dip will be maximum. (2) Magnetic declination: The small angle between the magnetic axis and geographic axis at a place is defined as magnetic declination at that place. It is represented by θ . (3) Horizontal component: It is the component of the earth’s magnetic field along the horizontal direction. So the angle of dip is the angle between the earth’s magnetic field i.e. B and the horizontal component i.e. B H .

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 5 - Magnetism and Matter>assam board-2019>Q 3

EASY

12th Assam Board

IMPORTANT

Earn 100

What did Meissner actually observe which is known as Meissner effect?

Important Questions on Magnetism and Matter

MEDIUM

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 5 - Magnetism and Matter>assam board-2019>Q 4

A magnetic dipole is oscillating in a magnetic field obeying the following expression

$\frac{d^{2} θ}{{dt}^{2}} = - \frac{mB}{I} θ$ :

What is the time period of oscillation and mention the nature of oscillation?

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12th Assam Board

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 5 - Magnetism and Matter>assam board-2020>Q 5

Of two metals A and B, it is found that $χ_{A} > > 1$ and $- 1 \leq χ_{B} < 0$ . Name the types of materials to which the metals A and B do belong. Give one example of each.