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Notes on Magnetism 1. A magnet is any substance that attracts iron. ( That a mgnet attracts other substances is true but that it attracts iron is sufficient to call it a magnet ). 2. The following observations were made about magnets 3. (i) The attraction is maximum at two points in the magnets. (These points are named as poles of the magnets and the line segment joining these points is named as the axis of the magnet. (ii) When a magnet is suspended freely with the magnetic axis parallel to the groung, one particular pole always tries to point out in the north direction. This pole is named as the north seeking pole of the magnet or simply north pole of the magnet. Obviously, we have no choice but to call the other pole as south pole. (iii) Likes pole repel and unlike poles attract (iv) There are no magnets with single pole. If a magnet is broken into two pieces , each piece automatically acquires two ples. (v) The force of attraction or repulsion between two poles is found to be inversely proportional to the sqyuare of the distance between them (Weber?). (vi) The force with which a north pole is repelled by a north pole of a magnet is same as the force with which the south pole of the same magnet is attracted by the given north pole. So, we may have both the poles of the magnet have same strength for attraction and repulsion. Now, the question is, is it possible to define the above mentioned strength of the magnet ? Remember, measuring means comparing. To do this we must first make a postulate that every pole of a magnet has what may be called pole strength which is indicative of its ability to attract or repel other poles. First, we need to define the equality of pole strengths. This is quite easy. Two pole strengths are said to be equal if both of them attract or repel a given pole from a given distance with the same strength. Suppose A,B,C are three poles. Suppose A attracts C with twice the force as B attracts C. Now, I may define the pole strength of A to be twice that of B. In so defining, the force between two poles becomes proportional to the product of the pole strengths. The above definition is not a random one but in tune with the observations. What remained is to define the unit of the pole strength. 4. For a moment let us call m and n as the pole strengths of two poles separated by a distance d and the force between them is found to be F. So far, we found that πΉ β ππ/π 2 . i.e., = πππ/π 2 . If we assume that the force between poles of magnet depends on pole strength and their separation alone, it would be convenient to define unit of pole strength in such a way that k becomes 1. ( We did likewise in defining unit of force). We may define a unit of pole strength as β two poles of equal strengths are said to be having a pole strength of one unit if they exert a force of 1 Newton when separated by 1 meterβ. This unit may be called one Tom. 5. A magnetic field is said to exist in a region or space if a magnet experiences a force (obviously magnetic force) at that region.Just like it became important for us to measure pole strength, it is very much important for us to measure magnetic field because at different points the magnetic forces are different.The question how much is the field is more important than whether field exists or not. We quantify the magnetic field as follows: To every point in the magnetic field, we associate some strength and direction i.e., with every point in the magnetic field we associate a vector. The magnitude of the field at pont may be defined as the force experienced by a pole of unit pole strength. The direction of the field , by convention, shall be taken as the direction of motion of north pole at that point.This vector is usually represented as β and is called the π΅ Magnetic Field Vector at the point. ( For historical reasons, this vector has so many names). Obviously, the unit of β is Newton per Tom. π΅ 6. A magnetic line of force, by definition, is the path traced by a north pole. By this definition, the following things are implied (i) A MLF starts from north pole and ends in south pole. (ii) No two MLFs intersect (iii) The magnetic field vector at any point on a MLF is tangential to that point. Why do we need MLFs at all? 7. Actually, at any point in region or space, where there a magnetic field, there is an MLF. But if we draw all these MLFs, we do not get lines at all, let alone the lines βrepresentingβ the field. So, magnetic lines are drawn in such a way to indicate the strength, direction and variation of magnetic field. Lines of force drawn such that the number of lines passing norm,al to an area per unit area gives the magnitude of field strength at that point. The number of lines passing through an area is called that magnetic flux through the area. The magnetic flux per unit area is called flux density. So, by definition, numerically, magnetic field strength is same as flux density. 8. In 1600, Gilbert realised that earth itself is a magnet. 9. The year 1819 changed the whole story of Magnetism. While Oersted discovered that a moving charge produces a magnetic field, Ampere, later, realised that moving charge alone produces a magnetic field. In a way, magnetic field became more fundamental than magnet.Various questions arised which can be put into two categories (i) Magnetic effects of moving charges (ii) Behaviour of a moving charge in a magnetic field. While Lorentz quantified the second aspect, Biot & Savart quantified the first aspect. Because magnetic field assumed significance over magnet, the unit of magnetic field is first defined and the pole strength is then defined in terms of unit of magnetic field strength. 10. It is observed that a charged particle at rest do not experience any force. But if a charged particle with is moving with a velocity β in a magnetic π£ field β then a force is experienced by that particle which is perpendicular π΅ to the plane containing vectors representing β and β (By observation). π£ π΅ It is also found that the force acting on the particle is proportional to the charge of the particle, speed of the particle and magnetic field strength. So, the force on the particle is given as ππ(β × β ), where k is a constant π£ π΅ of proportionality. Now, the unit of magnetic field is defined in such a way that k becomes 1. β A magnetic field which produces a force of one newton on a charge of one coulomb moving at a speed of one metre per seond is defined to be magnetic field of one unit.βThis unit of magnetic field is called Tesla. We can observe that Tesla is Newton per Amp.Met. Because magnetic field is defined as force per unit pole strength, pole strength is the magnetic force per unit magnetic field.So, the unit of pole strength is necessarily N/T viz. N/(N/A.m) viz. A.m.It now remains to relate unit of pole strength i.e., A.m with 1 Tom. Rather that relating A.m and Tom we change k in point 4. It was observed that the value of k actually depends on the material that separates the poles. If no material is present ( if vaccum is present) , k is found to be 10β7 π/π΄2 and this value is given a special name ( absolute permeability) and a special symbol (ππ ).