Magnetism and Matter | Class 12 Physics Notes

5.2 THE BAR MAGNET

The bar magnet is a fundamental magnetic object exhibiting two poles: north and south. When iron filings are sprinkled on a sheet of glass placed over a bar magnet, they arrange themselves in a pattern that reveals the magnetic field lines. This pattern suggests that the bar magnet behaves like a magnetic dipole, similar to an electric dipole with positive and negative charges. The north pole of the magnet points approximately towards the geographic north when suspended freely, and the south pole points towards the geographic south. A similar pattern of iron filings is observed around a current-carrying solenoid, indicating analogous magnetic behavior. This section introduces the concept of magnetic field lines as a visual representation of the magnetic field around magnets and current-carrying conductors. The magnetic field lines form continuous closed loops, unlike electric field lines which begin and end on charges. The tangent to a magnetic field line at any point gives the direction of the magnetic field vector at that point. The density of field lines indicates the strength of the magnetic field; more lines per unit area mean a stronger field. Importantly, magnetic field lines never intersect, ensuring a unique direction of the magnetic field at every point. The bar magnet can be thought of as an equivalent solenoid, consisting of many tiny current loops producing a magnetic dipole field. This analogy is supported by the similarity in magnetic field patterns and can be tested by observing the deflection of a small compass needle near a bar magnet and a current-carrying solenoid, which are similar. The axial magnetic field of a finite solenoid at large distances resembles that of a bar magnet, with the magnetic moment of the bar magnet equal to that of the equivalent solenoid producing the same field. When a small magnetic dipole with magnetic moment m is placed in a uniform magnetic field B, it experiences a torque τ = m × B that tends to align the dipole with the field. The magnetic potential energy of the dipole in the field is U_m = -m · B, with the zero of potential energy chosen when the dipole is perpendicular to the field. The potential energy is minimum when the dipole aligns with the field (stable equilibrium) and maximum when it is opposite (unstable equilibrium).

📊 Diagram: FIGURE 5.1 The arrangement of iron filings surrounding a bar magnet. The pattern mimics magnetic field lines. The pattern suggests that the bar magnet is a magnetic dipole; (a) Bar magnet field lines; (b) Current-carrying finite solenoid field lines; (c) Electric dipole field lines. At large distances, the field lines are very similar. The curves labelled ① and ⑪ are closed Gaussian surfaces; (a) Calculation of the axial field of a finite solenoid to demonstrate similarity to a bar magnet; (b) A magnetic needle in a uniform magnetic field B used to determine B or magnetic moment m of the needle.

🧪 Activity: Placing a small magnetic compass needle at various points around a bar magnet and a solenoid to observe and plot magnetic field lines.

🔗 Connection: Leads to the electrostatic analog of magnetic dipoles and Gauss's law for magnetism.