Tiêu đề 20.Magnetism and Matter-F.pdf ✅

NEET-2022 Ultimate Crash Course PHYSICS MAGNETISM AND MATTER
Important Points to Remember 1. The tangent to a magnetic field line at a point gives the direction of the net magnetic field acting at that point. 2. Magnetic field lines are always closed paths, whatever may be the source of magnetic field. Hence, there is no beginning or end point for a magnetic field line. There are no sources or sinks for magnetic field lines in a magnetic field. That is, there is no isolated magnetic pole. 3. The magnetic field lines can never intersect. 4. The number of magnetic field lines across unit area in a region of space is a measure of the strength of the
magnetic field in that region. 5. The configuration of field lines of the magnetic field produced outside a bar magnet resemble that of the electric field lines around an electric dipole as shown in Fig. (a) and (b). 6. There can be magnets without poles. A toroid and a solenoid of infinite length have magnetic Properties but have no poles. 7. The magnetic field due to a small bar magnet at a point. P, at a distance r from the centre of the magnet and at angle  with the magnetic axis is 0 2 3 m B 3cos 1 4 r  =   +  The direction of field makes an angle a with the line OP such that 1 tan tan 2  =  8. For a point P on the axis is of a short bar magnet the field is 0 a 3 2m B 4 r  =   9. For a point P on the equatorial line of a short bar magnet the field is 0 e 3 m B 4 r  =   10. The field at a certain distance along the axis of a short bar magnet is twice that at the same distance along the equatorial line. 11. If n is the number of turns per unit length then, N n l = 2 12. At a distance r from the center 0 of the solenoid, 13. The total magnetic field at point P due to the entire solenoid 2 0 3 2 P NIa B r  = (for r >> l and r >> a).
14. If the radius a of the solenoid is very small compared to r, we get 0 3 2 4 P NIA B r   =  where 2 A a =  is area of cross section of the solenoid 0 3 2 4 P m B r   = -------------(1) where m = NIA is magnetic moment of the solenoid. This equation is similar to the equation for the magnetic field due to a short bar magnet on the axial line 0 3 2 4 P m B r   = ----------(2) m represents the magnetic moment of the magnet, which is the product of its pole strength and magnetic length. The resemblance of Eqs., (1) and (2) reveal the equivalence of a solenoid and a bar magnet. 15. Magnetic moment m n l IA nIA l = = (2 2 ) ( ) i.e., m nIA l = (2 ) --------------(3) 16. The electric field on the axial line of a short dipole is given by a similar equation. 3 0 1 2 4 P E  r = ------------(4) where p is the electric dipole moment given by p q l = (2 ) ------------(5) 17. Comparing Eqs., (3) and (5) we observe that the quantity nIA can be regarded as the magnetic analogue of electric charge. It is sometimes called magnetic charge or pole strength. By convention, the positive pole of the magnet having a pole strength + = q nIA m ( ) is referred to as the N- pole middle negative pole of strength m −q is referred to m the S-pole. 18. The magnet experiences a torque given by   = mBsin or  =  m B 19. The-torque-tends—to rotate the bar magnet until its axis becomes parallel to the applied field. 20. A magnet has a tendency to align along the direction of external magnetic field B . Work has to be done in rotating the magnet. The work done in rotating the magnet from  = 1 to  = 2 is given by W mB = − (cos cos   1 2 ) 21. The work done in rotating the magnet is stored as potential energy. The potential energy of a magnet inclined at angle  with the external field B is given by U mB = − cos 22. If a magnet suspended in a uniform magnetic field is slightly displaced, it performs torsional oscillations. The period of oscillation is given 2 I T mB =  . I is the moment of inertia of the magnet about the suspension axis 23. The net magnetic flux across any arbitrary closed surface in a magnetic field is zero. i.e., B dS . 0 = 