Magnetism PDF

# 12. Magnetism ## Introduction * William Gilbert (1544-1603) was the first to systematically investigate the phenomenon of magnetism using the scientific method. * He also discovered that Earth is a weak magnet. * Danish physicist Hans Oersted suggested a link between electricity and magnetism....

# 12. Magnetism ## Introduction * William Gilbert (1544-1603) was the first to systematically investigate the phenomenon of magnetism using the scientific method. * He also discovered that Earth is a weak magnet. * Danish physicist Hans Oersted suggested a link between electricity and magnetism. ## Basic Properties * Magnetic poles always exist in pairs. The pole of a magnet can never be separated, meaning a magnetic monopole does not exist; we always have a magnetic dipole. * Two poles called the north pole and south pole. * If a magnet is broken into two or more pieces, then each piece behaves like an independent magnet. * Like magnetic poles repel each other. * Unlike (opposite) poles attract each other. * When a bar magnet/magnetic needle is suspended freely, it aligns itself in the geographically north-south direction. ## Magnetic Lines of Force and Magnetic Field 1. Magnetic lines of force of a magnet or a solenoid form closed loops. This contrasts with the case of an electric dipole. 2. Magnetic lines of force originate from the north pole and end at the south pole of a bar magnet. 3. **Outside of the magnet:** The line of force direction is from N to S. 4. **Inside the magnet:** The line of force direction is from S to N. 5. **Direction of net magnetic field at a point:** The tangent to the magnetic line of force at that point. 6. **Magnitude of magnetic field:** The number of lines of force crossing per unit area decides the magnitude of the magnetic field. 7. **Magnetic lines of force do not intersect.** 8. **Magnetic flux (Φ):** The number of magnetic field lines passing through any surface placed in a magnetic field. (The density of lines of force, i.e., the number of lines of force per unit area normal to the surface around a particular point). 9. The strength of the magnetic field at that point is determined by the magnetic flux. * **Φ ∝ B** * **Φ = BA** * **S.I unit:** weber (Wb) * **Φ = BAcosθ** 10. **Magnetic field (B) :** B = Φ/A = magnetic flux/Area * The magnetic field is the ratio of magnetic flux per unit area. * **S.I unit:** wb/m² or Tesla. * 1 Tesla = 10⁴ Gauss ## Bar Magnet * A bar magnet is an example of a magnetic dipole. A magnetic dipole is a pair of two magnetic poles of opposite types and equal strengths a finite distance apart. * A bar magnet is an example of a magnetic dipole. * **Geometric Length** * **Magnetic Axis:** the line passing through both poles of a bar magnet. (There is only one axis for a bar magnet). * **Magnetic Equator:** a line passing through the centre of a magnet and perpendicular to its axis is called a magnetic equator. * **Equatorial plane:** the plane containing all equators is called the equatorial plane. Points on the equatorial plane are equidistant from the centre of the magnet. * **Equatorial Circle:** the circle that is the equatorial circle. * **Magnetic Length (2l):** the distance between the two poles of a magnet. * Magnetic Length (2l) = (5/6) * Geometric Length * **Magnetic Field Due to a Bar Magnet at a Point Along its Axis:** Consider a bar magnet with: * South Pole (S) * North Pole (N) * Point (P) * Where NP = r - l * Where SP = r+l * The bar magnet's magnetic field at the point P is: * **B_a = (μ₀ * 2m)/(4π * r³) ** * The bar magnet's magnetic field is analogous to an electric field. * If the distance **r >> l** then the terms can be neglected. Therefore: * **B_a = μ₀ * 2m / (4π * r³) ** * Here, * **μ₀ = Permeability of free medium** * **ε₀ = Permittivity of free medium** * **Magnetic Field Due to a Bar Magnet at a Point Along its Equator:** * Consider a bar magnet with: * South Pole (S) * North Pole (N) * Point (P) * Where the distance from either pole to point P is r. * The bar magnet's magnetic field at the point P is: * **B_eq = -μ₀ * m / (4π * r³) ** * The -ve sign shows that the direction of the magnetic field on the equator is opposite to the direction of the magnetic field along the magnetic axis. * **B_eq = -μ₀ * m / (4π * r³) ** * This is analogous to an electric field. * If you compare B_eq with B_a then: * **B_a = μ₀ * 2m / (4π * r³) ** * **B_axis = 2 * B_eq ** * **Magnetic Field Due to a Bar Magnet at an Arbitrary Point:** * Consider a bar magnet with: * South Pole (S) * North Pole (N) * Point (P) * Where the distance from the centre to point P is r. * θ is the angle between r and the axis of the bar magnet. * The component mcoso along r is the axial point. * The component msine perpendicular to r is the equatorial point at the same distance. * **Axial Magnetic Field:** **B_a = μ₀ * 2mcosθ / (4π * r³) ** * **Equitorial Magnetic Field:** **B_eq = μ₀ * msine / (4π * r³) ** * **Magnitude of the Resultant Magnetic Field B at point P:** * **B = √(B_a² + B_eq²)** * **B = μ₀ * m / (4π * r³) * √(cos²θ + sin²θ)** * **B = μ₀ * m / (4π * r³) * √1** * **B = μ₀ * m / (4π * r³) * √(cos²θ + sin²θ)** * **B = μ₀ * m / (4π * r³) * √1** * **B = μ₀ * m / (4π * r³) ** * **Direction of the Resultant Magnetic Field:** * **tan x = Y/X = B_eq / B_axis = μ₀ * msine / (4π * r³) / μ₀ * 2mcosθ / (4π * r³) ** * **tan x = (sinθ) / (2cosθ)** * **tan x = (1/2) tan θ** ## Gauss' Law of Magnetism * **Statement:** The net magnetic flux ΦB through a closed Gaussian surface is zero. * **ΦB = ∫SB.ds = 0** * **Explanation:** * There are Gaussian surfaces S1, S2 * The number of magnetic field lines entering each of the surfaces S1 and S2 are equal to the number of lines leaving the respective surfaces, meaning the net flux ΦB through them is zero. ## Earth's Magnetism * If a bar magnet hangs freely, the bar magnet shows the north-south direction. * It proves that earth has a weak magnet. * The magnetic field is present on Earth everywhere, called terrestrial magnetism. * The magnetic field of the Earth is caused by the movement of molten iron in the Earth's core. This movement creates electric currents that produce a magnetic field. * **Diagram:** * **MM:** Magnetic Axis * **AA:** Magnetic Equator * **The straight line NS:** the magnetic axis (MM). * **Geographic meridian:** a plane perpendicular to the surface of the Earth. * **Magnetic meridian:** a plane perpendicular to the surface of the earth and passing through the magnetic axis is the magnetic meridian. * **Magnetic declination (δ):** the angle between the geographic and the magnetic meridian at a place. The declination is small in India. * **Magnetic inclination (Φ) or angle of dip:** the angle made by the direction of the resultant magnetic field with the horizontal at a place is the inclination or the angle of dip at the place. * **Earth's magnetic field:** The magnetic force experienced per unit pole strength is the magnetic field B. * The magnetic field B can be resolved into components along the horizontal (BH) and along the vertical (BV). * The two components can be related with the angle of dip (Φ). * BH = BcosΦ * BV = BsinΦ * tanΦ= BV / BH * **Special Cases:** * At the magnetic north pole: B = BV, directed upward. * BH = 0, Φ = 90° * At the magnetic south pole: B = BV, directed downward. * BH = 0, Φ = 270°