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[TOPIC 1] Magnetic Dipole g, , Field Lines, , A magnet is a material or an object that produces, a magnetic field. The magnetic field is invisible, but is responsible for most notable property of, magnet., , 1.1 Force Between Two, Magnetic Poles, , Magnitude of force acting between two magnetic, poles is given by, , , , , , , , -™m +Mo2, Ss N, Sr, Rain, 7, or k= Ho, 4n, , where, m, and my, are magnetic strength of poles, and k is m,, , 1.2 Magnetic Field Lines, , These are imaginary lines which give pictorial, , Tepresentation for the magnetic field inside and, around the magnet., , ‘agnetic force constant. Its SI unit is A-m., , Nd Magnetic, , B, , (i), , :, , Their properties are given as below:, , Axis, , , , , , , , , , (i) These lines form continuous closed loops., , (ii) The tangent to the field line at a particular, point gives the direction of the field at that, _ point., , (iii) Larger the density of the lines, stronger will, be the magnetic field., , (iv) These lines do not intersect one another., , 1.3 Magnetic Dipole, , An arrangement of two equal and opposite, magnetic poles separated by a small distance., , e.g. A bar magnet.

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Magnetic Dipole Moment (Mm), , It represents the strength of magnets. The, magnetic dipole moment of a magnetic, dipole is, , , , , , given by M=mx2/, , where, is pole strength and 2/ is dipole, length directed from S$ to N., , , , , , , , , , , , —m +m, s N, —21—ai, , The SI unit of magnetic dipole moment is AnV’ or J/T. It is a vector quantity and its, direction is from South pole to North pole., , Magnetic field strength at a point, due to a bar magnet at, , (i) On axial line (end-on-position), , @ rs), , , , The direction of magnetic field is, along the direction of magnetic dipole, moment (M)., , (ii) On equatorial line, (broadside-on-position), , , , , , Equatorial, line, , , , The direction of magnetic field is, parallel to the magnetic dipole and, opposite to the direction of dipole, moment., , 1.4 Torque ona Bar Magnet ing, Uniform Magnetic Field, , eld B is represented by equidistay, , i netic fi oe, , aT eee is a bar magnet of lengt, par / it, strength of each pole is M., , no=-MxB, Torque, t= MBsin e=M M, , , , , , where, 0 is the angle between M and B. Its SI unit is, , -1, joule per tesla (JT). ;, <... = MB, when dipole is perpendicular to the field ang, , oe when dipole is parallel or anti-parallel to the field,, , Potential Energy of a Magnet Dipole, (Bar Magnet) in a Magnetic field, , Potential energy of a magnetic dipole in a magnetic field, is given by, , U=- MBcos8 =-M-B, , , , , , , , , , where, 9 is the angle between M and B., , Work done in rotating the dipole in a uniform magnetic, field from 0, to 8, is given by, W = MB (cos 8, — cos 83), , The direction of dipole moment can be obtained by right, hand thumb rule. Its $I unit is A-m2., , NOTE Current loop behaves lik, is given by M= 1a,, , Oscillation of q Freely, Suspended Magnet, , . , Magnetic fi i, time period of oscillation, Held are in SHM. The, , where, J = moment of ;, : Of inertia of t, M = magnetic Moment he magnet,, , and B= magnetic fj, , eld intensity., , ‘© a magnetic dipole whose dipole moment |

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c Dipole Moment, , ment of a revolving electron is, , netic dipole Mor, , , , Mag), given by ., evi, M=— oF, 2, here, vis the speed of electron on a circular path, where, V, , fradius r. 2 is angular momentum and given as, ol ra :, , Lemur., , , , , , Orbital magnetic moment, of o revolving electron, , 1.6 Force Between two, Magnetic Dipoles, , Mutual force of interaction between two magnetic, dipoles is given by, , , , 4n r, , where, M, and M. 2 are magnetic dipole moments, of two different magnets., , Bar Magnet as an, Equivalent Solenoid, , The expression of magnetic field at distance r from, centre is given by, , , , Thi Nisan & 2x. Seth, S expression is equivalent to that of bar, Magnet., , 1.7 The Electrostatic, Analogue, , The magnetic an..., dipole comeing Pole is analogous to an electric, Sisting of two equal charges of opposite, , sign (4, a 8 : 9) Seprated by a certain distance (a). It has, N electric dipole Moment, , P = 4a), , , , The Dipole Analogy, , , , , , , , mee Space _Electrostatics Magnetism,, oustant (eo) (Ho), , _Dipole moment / p M, , Equatorial field = ey 3 -[L)M/4nr2, , fora short dipole = eee, , Axial field for a 2p /4negr? [p2M/4nr>, short dipole, , External field : pxE MxB, , Torque, , External field : —p-E —M-BY, Energy \, , , , Magnetism and Gauss’ Law, , The net magnetic flux (9g) through any closed, surface.is always zero., , , , This law suggests that the number of magnetic, field lines leaving any closed surface is always, , equal to the number of magnetic field lines, , entering it., , , , o, =2B-AS=0 =>, B-AS=0