Tiêu đề SP-4_Ch-20_Magnetism and Matter.pdf ✅

Chapter Contents Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Introduction Bar Magnet Magnetism and Gauss’s law Earth’s Magnetism Magnetisation and magnetic Intensity Magnetic properties of Materials Introduction The science of magnetism grew from the observation that a certain ores could attract small pieces of iron and pointed in certain direction when kept on floating cork. The ore as originally found in the district of Magnesia in Asia minor (now in western Turkey) and therefore named magnetite. The word magnet owes its origin to this island of Magnesia. Since 400 BC Chinese had been using magnetic needles to determine directions while sailing. BAR MAGNET (a) The bar magnet has poles similar to the positive and negative charge of an electric dipole. (b) One pole is designated as north pole and other as south pole. (c) When suspended freely, these poles point approximately towards the geographic north and south poles. (d) Like poles repel each other and unlike poles attract each other. (e) The poles of a magnet can never be separated. Magnetic Field Lines (1) Magnetic field line is an imaginary curve, the tangent to which at any point gives direction of magnetic field B at that point. (2) The magnetic field lines of a magnet (or of a solenoid carrying current) form close-continuous loops. (3) Outside the body of magnet, the direction of magnetic field lines are from north pole to south pole. (4) No two magnetic field lines can intersect each other. (5) Larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B. (6) Magnetic lines of force come out and go into a magnetic material at any angle. Chapter 20 Magnetism and Matter
52 Magnetism and Matter NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 (7) Uniform magnetic field Non-uniform magnetic field Non-uniform magnetic field Pole strength of magnetic charge (i) Just like electric charges, a magnetic charge (also called pole strength) +m is assigned to the north pole and –m to the south pole of a bar magnet. If length of the bar magnet is 2l, then its magnetic moment is given by M ml  (2 ) [Following electrical analogy] Magnetic moment is a vector quantity and its direction is from south pole to north pole. (ii) Magnetic field strength due to a magnetic pole (hypothetical) at a distance r is given by 0 2 4 m B r    (iii) Unit of pole strength or magnetic charge (m) is ampere-metre. (iv) A consequence of the fact that magnetic monopoles do not exist is that the magnetic field lines are continuous and form closed loops. In contrast, the electrostatic lines of force begin on a positive charge and terminate on the negative charge. (v) If a magnet is divided into two equal parts such that the cross-sectional area becomes half, each part will be a magnet with half the pole-strength of the original magnet [Figure (b)]. +m m 2l M = m l × 2 (a) m/2 m/2 2l m/2 m/2 M = l  × 2 m 2 M 2 = (b) +m m l +m m l M 2 M ml =  = (c) In the figure (c), the original magnet [(figure (a)] has been cut into two equal parts with the cross-section remaining unchanged. In this case each part is a magnet with the original pole-strength m. (vi) A steel rod has a magnetic moment M. If it is bent into a semicircular arc, find its magnetic moment. Suppose m = pole-strength L = Length of the rod M = mL L + m  m (a) The magnetic moment M = mL When the rod is bent in a semicircular arc of radius r, r = L or,   L r The new effective length = 2r =  2L  2r m + m (b) The new magnetic moment is MmL Lm rmM       2 )( 22. 2 (vii) Two identical magnets each of pole-strength +m –m –m m and length L, are joined perpendicularly to +m each other as shown in the figure.
NEET Magnetism and Matter 53 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 The magnetic moments M1 and M2 of the two magnets are shown in the Figure. Vectorially M is the resultant magnetic moment where 2 2 2 1  MMM = 2 2  mLmL )()( = 2mL M M1 M2 Its direction bisect the angle between M1 and M2 Coulomb’s law of magnetism Though isolated monopoles does not exist but idea of monopole is quite useful in understanding magnetic interaction between magnets. Let pole strength of a monopole be m, then magnetic force between two isolated poles kept at separation r is 1 2 2 m m F r   r m1 m2 0 1 2 4 m m F 2 r     Attractive if one pole is North and other South. Repulsive if both poles are of same type ( North-North or South-South) i.e. Magnetic field due to a monopole (i) Magnetic field due to monopole at a point is equal to magnetic force experienced by a unit pole strength if kept at that point. 0 Fm B m P P N-pole S-pole r r m –m B B 0 2 4 m B r    It is away from pole if it is -pole. N It is towards pole if it is -pole. S (ii) Magnetic dipole moment of a bar magnet. It is equal to the product of any one pole strength and separation between 2l –m m two poles. Mm l   2 Directed from South-pole to north-pole. Magnetic field due to a bar magnet (A) On axial position. Baxial = 0 2 22 2 4 ( ) M r r l     S-pole N-pole –m +m P B2 B1 Baxial r l l For short bar magnet r > > > l 0 axial 3 2 4 M B r    It is along magnetic dipole moment.
54 Magnetism and Matter NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 (B) On normal bisector. 0 3 2 2 2 4 ( ) M B r l      S-pole N-pole P B1 B2 r    ( + ) r l 2 2 1 2 ( + ) r l 2 2 1 2 The field will be opposite to dipole moment. For short bar magnet r > > > l 0 3 4 M B r     Note : For short bar magnet B 2B axial   Torque on a magnetic dipole in uniform magnetic field (i) A magnet of dipole moment M is kept so that it makes angle  with uniform magnetic field B. M B B B FN FS 2L  N S 2 sin L   M B    | | sin MB    ( is angle between M B and   ) M B B S N  F = 0 Net B B M S N Max F = 0 Net M N S  F = 0 Net (a) (b) (c) Stable equilibrium If magnetic dipole is slightly disturbed from equilibrium position and released, then it will oscillate with time period  2 l T MB Work done in Rotating a Magnetic Dipole in Uniform Magnetic Field (i) Let at an instant dipole is at  from magnetic field, then the torque acting on dipole is  = MB sin  M S-pole N-pole  (ii) In order to rotate dipole against this torque by d angle, work is done on it by some external source. dW =  d dW = MB sin  d Work done on dipole to rotate it from initial orientation 1 to final orientation 2 is