Title 17. Magnetism and Magnetic Effects of Current.pdf ✅

Magnetism and Magnetic Effects of Current Magnetism and 365 Magnetic 17 Effects of Current QUICK LOOK A small number of crystalline substances exhibit strong magnetic effects called ferromagnetism. Some examples of ferromagnetic substances are iron, cobalt, nickel, gadolinium, and dysprosium. These substances contain permanent atomic magnetic moments that tend to align parallel to each other even in a weak external magnetic field. Paramagnetic substances have a small but positive magnetism resulting from the presence of atoms (or ions) that have permanent magnetic moments. These moments interact only weakly with one another and are randomly oriented in the absence of an external magnetic field. When an external magnetic field is applied to a diamagnetic substance, a weak magnetic moment is induced in the direction opposite the applied field, causing diamagnetic substances to be weakly repelled by a magnet. Table 17.1: Comparative Study of Magnetic Materials Property Diamagnetic substances Paramagnetic substances Ferromagnetic substances Cause of magnetism Orbital motion of electrons Spin motion of electrons Formation of domains Behaviour In a non- uniform magnetic field These are repelled in an external magnetic field i.e. have a tendency to move from high to low field region. These are feebly attracted in an external magnetic field i.e., have a tendency to move from low to high field region These are strongly attracted in an external magnetic field i.e. they easily move from low to high field region When the material in the form of liquid is filled in the U-tube and placed between pole pieces. Liquid level in that limb gets depressed Liquid level in that limb rises up Liquid level in that limb rises up very much the gaseous materials between pole pieces expands at right angles to the magnetic field. expands in the direction of magnetic field. rapidly expands in the direction of magnetic field Magnetic susceptibilit y χ and dependence on temperature Low and negative |χ| ≈ 1 Does not depend on temperature (except Bi at low temperature) Low but positive χ ≈ 1 On cooling, these get converted to ferromagnetic materials at Curie temperature Positive and high χ ≈ 102 These get converted into paramagnetic materials at Curie temperature Relative permeabilit y (μr) μr < 1 μr > 1 μr >> 1; μr = 102 Intensity of magnetisati on (I) very low low very high. I-H curves Magnetic moment (M) Very low (≈ 0) Very low Very high Examples Cu, Ag, Au, Zn, Bi, Sb, NaCl, H2O air and diamond etc. Al, Mn, Pt, Na, CuCl2, O2 and crown glass Fe, Co, Ni, Cd, Fe3O4 etc. Earth's Magnetic Field Figure: 17.1 Earth’s Magnetic Field As per the most established theory it is due to the rotation of the earth where by the various charged ions present in the molten state in the core of the earth rotate and constitute a current. At the poles and equator of earth the values of total intensity are 0.66 and 0.33 Oersted respectively. Magnetic axis and Geographical axis don't coincide but they make an angle of 17.5° with each other. The direction of earth’s Horizontal magnetic field is from south to North. At poles Horizontal Rotation axis Magnetic field lines North Geographical pole Magnetic axis S N W S E N H IS HS H +I H –I χ T TC χ T χ T N S Liquid N S Liquid N S Liquid Very strong N S Pushed in N S Pushed up N S
366 Quick Revision NCERT-PHYSICS component H(BH) = 0, while at equator vertical component V (BV) = 0. Magnetic Declination (θ): It is the angle between geographic and the magnetic meridian planes. Declination at a place is expressed at θ°E or θ°W depending upon whether the north pole of the compass needle lies to the east or to the west of the geographical axis. Figure: 17.2 Magnetic Declination Angle of Inclination or Dip (φ): It is the angle between the direction of intensity of total magnetic field of earth and a horizontal line in the magnetic meridian. Horizontal Component of Earth's Magnetic Field (BH) Earth's magnetic field is horizontal only at the magnetic equator. At any other place, the total intensity can be resolved into horizontal component (BH) and vertical component (BV). Also BH = B cosφ and sin B B V = φ . Therefore Earth’s magnetic field is 2 2 H V B B B = + and tan V H B B φ = Isolated magnetic poles do not exist. Magnetic dipole moment is a vector quantity; its direction is from south to north along the axis. Repulsion is the sure test to distinguish between a magnet and a piece of iron. Magnetic moment of bar-magnet M = m . 2l amp –m 2 where m = pole strength in amp-m, 2l = separation between poles. Figure: 17.3 If a rectangular bar magnet is cut in n equal parts then time period of each part will be 1 n times that of complete magnet (i.e. T T n ′ = ) while for short magnet T T n ′ = . If nothing is said then bar magnet is treated as short magnet. Figure: 17.4 Broken Magnet Magnetic moment of current loop is a vector quantity. Its direction is perpendicular to the plane of the loop. Magnetic moment of a current loop, M NIA = amp-m 2 . A dipole in a uniform magnetic field; Net force on dipole = 0 Torque on dipole τ θ = MBsin τ = × M B (vector form) Potential energy of dipole U MB M B = = − cos . θ (vector form ) Work done in rotating the dipole form equilibrium position ( 0 ) θ = ° through an angle θ. W MB = − (1 cos ) θ Magnetic Field: Magnetic field produced by a short magnetic dipole at axial position 0 3 2 . 4 M B r μ π = (axial position) At equatorial position, 0 3 . 4 M B r μ π = At any general point (r, θ) relative to centre of dipole 0 3 . 1 3cos 4 M B r μ θ π = + Force between to short magnetic dipoles (magnets) at separation r (magnetic moments M1 and M2) When they are co-axial, 0 1 2 4 6 . 4 M M B r μ π = When they are broadside on position, 0 1 2 4 3 . 4 M M B r μ π = Intensity of magnetization M I V = amp/meter; where V = volume. Magnetic susceptibility 1 ; m H χ = where H = magnetizing field in A/m 2 Absolute permeability, B H μ = Weber / Amp-meter Relative permeability, 0 1 r m μ μ χ μ = = + Curie law of paramagnetic substances, 1 m T χ ∝ Deflection magnetometer Tan A position (arms along E – W and magnet parallel to arms) 0 2 2 2 3 . tan 4 ( ) Md H d l μ θ π = − Tab B position (arms long N – S and magnet perpendicular to arms) 0 2 2 3/ 2 . tan 4 ( ) M H d l μ θ π = + S N S N S N S N S N L = 2l – m + m M Geographical Meridian Magnetic Meridian θ φ BV BH B N W E S θ θ°W θ°E θ
Magnetism and Magnetic Effects of Current 367 Vibration Magnetometer: If a small magnet is placed in magnetic meridian and vibrates in horizontal plane, the time period is 2 I T MH = π Where I = moment of inertia of magnet about axis of rotation 2 2 0 ( ) 12 M l b I + = (Where M0 = mass of magnet) If breadth of magnet is negligible 2 0 12 M l I = If a magnet is placed parallel to magnetic meridian and oscillates in vertical plane 2 2 I T MB = π If a magnet is placed perpendicular to magnetic meridian and oscillates in a vertical plane 2 I T MV = π Comparison of magnetic moments; Sum and difference method 2 2 1 1 2 2 2 2 1 2 M T T M T T + = − Magnetic moment of a current loop = NiA amp × m 2 where A = area of loop, N = number of loops Torque on a current loop in a magnetic filed τ θ = MBsin Where θ = angle between M and B ; In vector form τ = × M B In moving coil galvanometer, the pole pieces of a magnet are strong and cylindrical to make the field radial (sin 1). θ = Deflection of moving coil galvanometer is NBA i C θ = = ⇒ θ ∝ i Where C = torsional rigidity of suspension wire. Sensitivity of galvanometer: NBA i C θ = Galvanometer: Figure: 17.5 Tangent Galvanometer A normal galvanometer measures current. But a B.G measures charge due to impulse in the coil (sudden flow of charges for a short interval of time. A ballistic galvanometer measures the charge and its deflection is proportional to charge i.e. θ ∝ q. When the plane of vertical circular coil is in magnetic meridian, then i K= tanθ Where 0 2rH K μ N = = reduction factor r = radius of coil, H = horizontal component of earth’s magnetic field. A tangent galvanometer is most accurate when its deflection is 45°. Conversion of Galvanometer: With increase of range of ammeter, its resistance decreases. With the increases of range of voltmeter, its resistance increases. Out of voltmeter, ammeter and galvanometer, the resistance of voltmeter is largest and that of ammeter is smallest. Figure: 17.6 Working equation of conversion of galvanometer into ammeter. . g S i i S G = + Figure: 17.7 Shunt resistance . g g i S G i i = − The resistance of ammeter so formed. A SG R S G = + ⇒ R G A < Working equation of conversion of galvanometer into voltmeter. . g V i i R G = + Series resistance g V R G i = − Resistance of voltmeter so formed is RV = R + G. R G ig i Voltmeter i G Ig I-Ig S Ammeter I I Bar magnet Pointer Leveling legs Tangent Galvanometer Vertical coil θ θ H1 H Magnetic north
368 Quick Revision NCERT-PHYSICS Figure: 17.8 The voltmeter is a high resistance device so that it does not draw appreciable current from the circuit. A series resistor limits the current. The ohmmeter has a voltage source to drive a small current through the external resistance to be measured. It contains a calibration resistor. The ammeter has a parallel resistor of very small value to shunt most of the current away from the sensitive current measuring element. It must carry the total current of the circuit to be measured without appreciable voltage drop Hysteresis Curve: The complete cycle of magnetisation and demagnetisation is represented by BCDEFGB. This curve is known as hysteresis curve. Hysteresis energy loss = Area bound by the hysteresis loop = VAnt Joule; Where, V = Volume of ferromagnetic sample, A = Area of B – H loop P, n = Frequency of alternating magnetic field and t = Time Retentivity: When H is reduced, I reduces but is not zero when H = 0. The remainder value OC of magnetisation when H = 0 is called the residual magnetism or retentivity. Corecivity or corecive force: When magnetic field H is reversed, the magnetisation decreases and for a particular value of H, denoted by Hc , it becomes zero i.e., Hc = OD when I = 0. This value of H is called the corecivity. Magnetic hard substance (steel) → High corecvity Magnetic soft substance (soft iron) → Low corecivity Figure: 17.9 A Magnetic Field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field Magnetic flux cos . φ θ m = = BA B A weber Where B = magnetic field in Tesla, A = area of loop and θ angle between magnetic field and normal to loop. Magnetic force on a current carrying wire sin F Bil m = θ Where θ = angle between current element i l δ and magnetic field B Maximum force, F Bil m = when θ = ° 90 . When a current carrying wire is placed parallel to direction of magnetic field, the force on the conductor is zero. Figure: 17.10 Lorentz Force Magnetic Lorentz force on moving charge particle sin F qvB m = θ . Where θ = angle between velocity v and magnetic field B. F v B m = × (vector form) Lorentz force is perpendicular to both v and B. When a charged particle moves along the direction of magnetic field, the magnetic force on it is zero. Magnetic force between charges moving with velocity v1 and 2 v is weaker than electric force 1 2 2 m e F v v F c = Work done by magnetic force on charged particle is zero, therefore magnetic force changes only the direction of motion of charged particle. No magnetic force acts on a neutral/charge less particle. When charge q enters perpendicular to magnetic field. The path is circular having radius r given by 2 mv mEk r qB qB = = Where Ek = kinetic energy of particle. Time period 2 m T qB π = Curl fingers as if rotating vector v into vector B. Thumb is the direction for force. Point thumb in direction of velocity, fingers in magnetic field direction. Then plane direction is direction of force on charge B q V V F F S N q B North pole of magnet South pole of magnet F qv B = × Force is in direction that thumb points Force direction is outward from palm. B A G E F D C O I or (B) H I H Soft Iron Steel Ohmmeter RS G Voltmeter Ammeter Common Galvanomter R0 Rp RG