Magnetism and Mattery

Chapter 5 Magnetism and Matter Earth's Magnetism-Magnetic Dip and declination ➤ Earth's Magnetism-Magnetic Dip, magnetic declination Determination of Dip ➤ Apparent Dip Neutral Point, Tangent Galvanometer and Magnetic Intensity Neutral Point ➤ Tangent Galvanometer Oscillation Magnetometer ➤ Magnetic properties of matter- Intensity of Magnetisation Magnetic Properties of materials- Induction, Susceptibility and permeability Intensity of Magnetism Magnetic flux Magnetic Induction Magnetic Susceptibility Magnetic Permeability Classification of Magnetic Materials Electron theory Properties of Magnetic Materials & Hysteresis Ferromagnetism based on Electron theory Magnetic Susceptibility (x_m) of Ferromagnetic Materials (Curie - Weiss Law) Properties of Magnetic Materials- Diamagnetic materials Properties of Magnetic Materials- Paramagnetic materials Properties of Magnetic Materials- Ferromagnetic materials ➤ Hysteresis EARTH'S MAGNETISM-MAGNETIC DIP AND DECLINATION Earth's Magnetism - Magnetic Dip, magnetic declination The Earth naturally generates a magnetic field. This magnetic field has three main characteristics at any given point on the Earth's surface: (a) Declination This refers to the angle formed between the geographic meridian (a line passing through the Earth's poles) and the magnetic meridian (a line passing through the geomagnetic poles and a specific point on Earth's surface). (b) Inclination or Dip This is the angle formed between the Earth's magnetic field and the horizontal direction along the magnetic meridian. (c) Horizontal Component This component refers to the part of the Earth's magnetic field that lies in the horizontal direction along the magnetic meridian, pointing towards magnetic north. To illustrate these elements, one can draw a diagram starting from the geographic meridian, then drawing the magnetic meridian at an angle representing the declination. Along the magnetic meridian, the horizontal direction pointing towards magnetic north is specified. Geographical North Declination Vertical Geographical Meridian Magnetic North B Magnetic Meridian The magnetic field is at an angle 8 (dip) from this direction. The horizontal component BH and the total field B are related as BBcos & B=B/cos & By understanding these three elements of the Earth's magnetic field, one can determine both its strength (magnitude) and the direction it points. Ex. The horizontal component of the earth's magnetic field is 3.6 * 10 - 5T where the dip is 60 deg Find the magnitude of the earth's magnetic field. Sol We have BH = B * cos delta B = B_{H}/(cos 6) = (3.6 * 10 ^ - 5 * T)/(cos 60 deg) * 7.2 * 10 ^ - 5 * T Determination of Dipole Vertical Circular Scale(5) Magnetic Needle Horizontal Angular Scale(E) Spirit Level Levelling Screws When we adjust the setup using leveling screws and a spirit level, it's possible that the magnetic needle isn't aligned with the Earth's magnetic field direction, known as the magnetic meridian. The needle's orientation might deviate from the magnetic meridian by an angle ẞ, as depicted in the diagram. Consequently, the Earth's magnetic field (B_{epsilon}) differs in these two orientations. However, since both the needle's plane and the magnetic meridian share a common side where the vertical component exists, the vertical component (B_{nu}) is the same in both orientations. If & represents the angle of dip and B_{H}' is the horizontal component of the Earth's magnetic field along the plane of the needle, then B_{H}' = B_{H}*Cos*beta B_{H}' = B_{e}*Cos*theta*Cos*beta theta' is the angle of dip in the plane of needle, known as apparent dip. We have: B_{H}' = B_{c}*Cos*theta*Cos*beta Since the angle of dip for a specific location of Earth is a fixed quantity, B_{H}' in that location will be zero if and only if: Cosẞ0β = 90° This suggests that the angle between the plane of the needle and the magnetic meridian should be 90 deg for B_{H}' to be zero. Now, B_{H}' = 0 means the needle becomes vertical in its plane. Therefore, rotate the box till the needle becomes vertical and reads 90 deg - 90 deg on the vertical scale. In this position, B_{H}' = 0 Magnetic needle will be aligned with the vertical component (B_{nu}) of the Earth's magnetic field. In this position of the box, beta = 90 deg Thus, the magnetic meridian is 90 deg away from this orientation of the box. Therefore, rotate the box through 90 deg with the help of horizontal scale E to get the magnetic meridian plane. Measurement of dipole Now, the box and hence the vertical scale (where the needle is attached) is perfectly aligned along the magnetic meridian. Since the earth's magnetic field vec B lies in the same plane as that of the magnetic meridian, the reading on the vertical scale that the needle is now showing w.r.t the horizontal line directly gives the value of the dip. 2 Apparent Dipole When the plane of rotation of the magnetic needle is other than the plane of magnetic meridian then the dip obtained is known as apparent dip theta' Steps to find true angle of dip without knowing the location of magnetic meridian: When the arrangement of dip circle is just levelled perfectly, the needle will be in any arbitrary plane of rotation. Measure the apparent dip (theta') for this this plane of rotation of the magnetic needle Now, rotate the vertical scale of the dip circle arrangement by 90 deg This plane will be 90 deg away from the 1 st plane. Measure the apparent dip ( theta ^ prime prime )^ prime for this 2 ^ (nd) | plane. Therefore, B_{H}' = B_{H}*Cos*beta B = ẞcos ...(2) B H^ prime prime = beta_{H} * sin beta ...(1) B H ^ prime prime = B * cos theta * sin beta Squaring equation individually and adding them, we get. Now, we have: Cote= By B_{H} ^ prime prime =B V cot^ prime prime Substituting the values of B ^ r H and B ^ prime prime n in the above equation, we get, B_{v} ^ 2 * cot^2 (theta') +B v ^ 2 Cot^ 2 theta^ prime prime = beta^ 2 Cos^ 2 (Since cot^2 (theta') +cot^ 2 theta^ prime prime =cot^ 2 theta B v =B sin theta Rightarrow B/B_{V} = 1/(sin theta) \ cot^2 (theta') +cot^ 2 theta^ prime prime =cot^ 2 theta B H ^ prime2 +B H ^ prime prime2 = B ^ 2 * Co * s ^ 2 * theta beta_{H}' = beta_{v} * cot theta' cot theta ^ prime prime = B H ^ prime prime B y This expression helps one to know the value of true dip without knowing the magnetic meridian. 3 90 deg - beta \mathfrak{B_{n}} ^ prime prime 90 deg Magnetic Meridian B_{H} B H' B B_{H} B_{V} B Magnetic Meridian