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MAGNETISM AND, , MP, , , , > Current loop as a magnetic dipole and its magnetic dipole moment, magnetic dipole moment of a revolving, , electron, bar magnet as an equivalent solenoid, magnetic field lines; earth's magnetic field and magnetic, elements., , Revision Notes, , , , C, , Magnetic Dipole ), , Current loop as a magnetic dipole and its magnetic dipole moment, , r, , va, , v, , Magnetic dipole is a small magnet of microscopic dimensions similar to flow of electric charge around a loop., , Magnetic dipole moment is the strength of magnetic dipole that measures dipole’s ability to align itself with, external magnetic field., , Magnetic dipole moment, known as magnetic moment, is the maximum amount of torque generated by magnetic, force on dipole which appears per unit value of surrounding magnetic field in vacuum., , Magnetic field produced at large distance r from the centre of circular loop along its axis will be, , , , , , , , , , , , , , , , , , , , 2pglA ‘Scan to ki, p= Hon nore about, 4nr this topic, where, I = Current in the loop, A = Area [OPC, Magnetic moment of current loop is the product of current and loop area, fol, M=IXxA Magnetic, Movement, , , , A current loop may experience a torque in a constant magnetic field,, , ¥, t, , 32, = MxB, , Magnetic dipole moment of revolving electron, , >, , For an electron of charge ¢ revolving around a nucleus of charge Ze at an orbit of radius r, with velocity v and, magnetic moment j1;, the orbital magnetic moment will be, , , , But angular momentum of electron,, , , , WWW.JEEBC, , , , 2KS.IN, , Scanned with CamS
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MAGNETISM AND MATTER 65, , , , =, , 2m,, , Here (-) sign shows that angular momentum’s direction is opposite to the magnetic moment's direction, , , , Magnetic field of a Solenoid, Earth's Magnetism &, Magnetic properties of Materials |, , , , Bar magnet as an equivalent solenoid, , > Ifa solenoid of length 2/, radius a with current J having 1 number of turns per unit length, then the magnetic, moment of solenoid,, , M(=NiA), p= 402M, 4nd?, , , , > Magnetic moment of a bar magnet is equal to magnetic moment of an equivalent solenoid that produces same, magnetic field, , Gauss’ Law for Magnetic Fields, > Gauss’ Law for magnetism applies to the magnetic flux through a closed surface., > Itshows that no magnetic monopoles exist and total jlux through closed surface will be zero, , > The Gauss’s law for magnetic fields in integral form is given by, 6=[BdA=0, , Earth’s Magnetism, , , , , , > Farth shows magnetic properties. This, , , , s evident from the following facts: anes, more about, this topic, , © Availability of neutral points. At neutral points, magnetic field due to suspended magnet is | [aEaray, equal and opposite to the horizontal component of Earth's magnetic field. z, , @ A freely suspended needle stays in north - south direction., , , , , , , , , , > The source of Earth’s magnetism is still undefined, though certain theories have good scientific | |fm]#!, justifications like ions revolving with Earth. Earth’s Magnetic, Field, , , , , , , , Characteristics of Earth’s Magnetism, > Farth’s south pole and north pole are defined by Sun’s direction. These are known as geographical north and, south poles. Magnetic north and south poles are the points where the magnetic needle becomes perpendicular, to earth’s surface. Hence, there are two systems of directions., > Due to two systems of directions, we can draw two meridians. (Plane joining geographic North and South pole is, geographic meridian and plane joining, magnetic North and South pole is magnetic meridian), , , , Elements of earth’s magnetic field Scan to know, more about, , > Angle of Declination: At any place on Earth, the acute angle between magnetic meridian and the] __this topic, , geographical meridian is called the angle of declination El, > Angle of Dip: The angle of dip at any place is the angle between Earth’s magnetic field intensity =, , B with horizontal in the magnetic meridian at that place., , , , , , , , , , Angle of, Declination &, Dip, , , , , , , , , , Scanned with CamS
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66 Oswaal CBSE MC Qs Ouestion Bank Chapterwise for Term-I, PHYSICS, Class — XII, , ‘Angle of declination, , , , , , , , ST }—Angle of dip, Ay Barth's magnetic field, ata point Scan to know, more about, this topic, , , , | — Geographical meridian, , , , , , , , , , Elements of, Earth’s Magnetic, Field, , , , , , , , , , , , , , Magnetic merdian, , > Horizontal Component of Earth’s Magnetic field: The horizontal component of Farth’s magnetic field H is in the, horizontal direction in the magnetic meridian., By or H = Beos 0, , By = Bsin®, Where 0 is angle of Dip, tan0 = a, , HH, , We find the earth’s magnetic field B at any place by measuring its horizontal component. Hence,, , B= and By = Htan0, cos6, , > There is variation in magnetic field between place to place depending upon angle of Dip, angle of declination and, horizontal component of Earth, Hence, these are known as elements of Earth’s magnelic field., , , , Mnemonics, , , , Concept: Four characteristics of magnetic field lines:, , Mnemonics: I love new stories Tina found new Cookies., , , , Interpretation:, , (i) Imaginary Lines, , (ii) Extended North to South pole, , (iii) Tangent gives (magnetic) field direction, (iv) Never Cross each other, , , , Know the Formulae, > Magnetic field due to short dipole at distance ‘d’ on axial line:, , , , Boy = eM, 4nd°, > Magnetic field due to short dipole at distance ‘d’ on equatorial line:, =H, oul 4nd?, , STAND ALONE vel ek (1 Mark each), , , , , , Q.1. A toroid of n turns, mean radius R and cross- (A) is non-zero and points in the z-direction by, sectional radius a carries current I. It is placed on symmetry., a horizontal table taken as x-y plane. Its magnetic (B) points along the axis of the toroid (m = my)., moment m, , , , WWW.JEEBC, , , , 2KS.IN, , Scanned with CamS
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MAGNETISM AND MATTER, (C) is zero, otherwise there would be a field falling, 1 + a, as — at large distances outside the toroid., r, , (D)is pointing radially outwards., Ans. Option (C) is correct., , Explanation: As we know that a toroid can be, considered as a ring shaped closed solenoid. So, that itis like an endless cylindrical solenoid., , , , So, the magnetic field is only confined inside, the body of a toroid in the form of concentric, magnetic lines of force., , For any point inside, the emply space, surrounded by toroid and outside the toroid,, , the magnetic field B is zero because the net, current enclosed in these spaces is zero. So, thal, the magnetic moment of toroid is zero. In, general, if we take r as a long distance outside, , the toroid, the m x = but this case is not, r, , , , possible here., , Q.2. Consider the two idealized systems : (i) a parallel, plate capacitor with large plates and small, separation and (ii) a long solenoid of length L, R,, radius of cross-section. In (i), E is ideally treated, as a constant between plates and zero outside. In, (ii), magnetic field is constant inside the solenoid, and zero outside. These idealized assumptions,, however, contradict fundamental laws as below :, (A) Case (i) contradicts Gauss’s law for electrostatic, , fields., (B) Case (ii) contradicts Gauss’s law for magnetic, fields, (C) Case (i) agrees with f. Edl=0, (D) Case (ii) contradicts Hal =I,, Ans. Option (B) is correct., , Explanation: According to Gauss’s law of, electrostatic field,, , feds =, , So it does not contradict for electrostatic field as, the electric field lines do not form continuous, path., , According to Gauss’s law of magnetic field,, Bas =o, , It is clear that it contradicts for magnetic field, because there is magnetic field inside the, solenoid, and no field outside the solenoid, carrying current, but the magnetic field lines, form the closed paths., , Q3., , Ans., , Ans., , Ans., , Q7., , 67, , A rod of length L, along east-west direction is, dropped from a height H. If B be the magnetic field, due to Earth at that place and angle of dip is 0, then, the magnitude of the induced e.m.f, across two, ends of the rod when the rod reachs the Earth is, , (A) BLH cos 0 (B) BL cos 0 x (2gH)!*, , (C) BL cos 6/(2gH)'?_— (D) None of the above, . Option (B) is correct., Explanation: Horizontal component of, , magnetic field = B cos 0, Velocity of the rod = (2 gH)!, Induced e.m.f. = BLv = BL cos @ x (2 gH)!”, , . A coil of N turns and radius R carries a current I. It, , is unwound and rewound to make a square coil of, side a having same number of turns (N). Keeping, the current I same, the ratio of the magnetic, moments of the circular coil and the square coil is, , R? a, , (A) n> B) “5, , ) ms () we, R2, , © > (D) None of the above, a, , Option (A) is correct., , NIA., , a Asquare = pR? / 9?, , Maouare NIA,, , Explanation:, , ‘circular circular, , A magnetic dipole moment is a vector quantity, directed from:, , (A) South to North, (C) East to West, Option (A) is correct., , (B) North to South, (D) West to East, , Explanation: Magnetic dipole moment vector, is directed from South pole to north pole., , Time period of oscillation of a magnetic needle is, , (A)T= Po (B) T= 2x Pm, (C)T = 20 = (T= 2, , Option (B) is correct., Explanation: Time period of oscillation of a, ‘5 4 I, magnetic needle is T = 2n, , A magnetic needle is kept in a non-uniform, magnetic field experiences, , (A) a force as well as a torque, , (B) a torque but not a force, , (C) a force and a torque, , (D) a force but nota torque, , WWW.JEEBC, , , , JOKS.IN, , Scanned with CamS
