🔄 RECAP: Master 'Moving Charges & Magnetism' (Chapter 4) First:
Chapter 5: Magnetism and Matter
Vol 1: The Bar Magnet & Field Lines
Magnetism is not just about electric current. Certain materials (like Magnetite) naturally attract iron. This section deals with permanent magnets.
1. Magnetic Field Lines
Visual representation of the magnetic field vector.
Properties:
- Direction: North to South (Outside magnet), South to North (Inside magnet).
- Closed Loops: Unlike electrostatic field lines, magnetic field lines form continuous closed loops.
- No Intersection: Two lines never cross each other. If they did, there would be two directions of field at one point, which is impossible.
- Density: Crowded lines indicate a strong field.
2. The Bar Magnet as an Equivalent Solenoid
A bar magnet and a current-carrying solenoid produce identical magnetic fields.
Axial Field Formula: For a short magnet (dipole) of magnetic moment $m$ at distance $r$:
3. The Electrostatic Analog
We can compare magnetic quantities with electrostatic ones:
| Electrostatics ($1/\epsilon_0$) | Magnetism ($\mu_0$) |
|---|---|
| Dipole Moment $\vec{p}$ | Magnetic Moment $\vec{m}$ |
| Torque $\vec{\tau} = \vec{p} \times \vec{E}$ | Torque $\vec{\tau} = \vec{m} \times \vec{B}$ |
| Pot. Energy $U = -\vec{p} \cdot \vec{E}$ | Pot. Energy $U = -\vec{m} \cdot \vec{B}$ |
Vol 2: Earth's Magnetism
The Earth acts like a giant magnetic dipole. The dynamo effect (currents in the molten iron core) is the cause of this magnetism.
1. Elements of Earth's Magnetic Field
To completely describe the magnetic field at any place on Earth, we need three quantities:
(i) Magnetic Declination ($\alpha$)
The angle between the Geographic Meridian (True North) and the Magnetic Meridian (Magnetic North) at a place.
(ii) Angle of Dip or Inclination ($\delta$)
The angle that the Total Magnetic Field ($B_E$) of the Earth makes with the Horizontal surface.
• At Equator: $\delta = 0^\circ$
• At Poles: $\delta = 90^\circ$
(iii) Horizontal Component ($B_H$)
The component of Earth's total magnetic field along the horizontal direction.
$$B_H = B_E \cos \delta$$
$$B_V = B_E \sin \delta$$
$$\tan \delta = \frac{B_V}{B_H}$$ $$B_E = \sqrt{B_H^2 + B_V^2}$$
Vol 3: Magnetic Properties of Materials
Not all materials respond to magnets in the same way. We classify them into Diamagnetic, Paramagnetic, and Ferromagnetic.
| Feature | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Behavior in Non-uniform Field | Moves from Stronger to Weaker field (Repelled) | Moves from Weaker to Stronger field (Weakly Attracted) | Moves from Weaker to Stronger field (Strongly Attracted) |
| Susceptibility ($\chi$) | Small & Negative ($-1 \le \chi < 0$) |
Small & Positive ($0 < \chi < \epsilon$) |
Very Large & Positive ($\chi \gg 1$) |
| Effect of Temperature | Independent | Inversely Proportional ($\chi \propto 1/T$) | Decreases with Temp. Becomes Para above Curie Point. |
| Examples | Bismuth, Copper, Water | Aluminum, Sodium, Oxygen | Iron, Nickel, Cobalt |
Vol 4: Mission 100 Question Bank
Section A: MCQs (1 Mark)
Q1. At the magnetic north pole of the Earth, the value of the angle of dip is:
(a) $0^\circ$ (b) $45^\circ$ (c) $90^\circ$ (d) $180^\circ$
Ans: (c) $90^\circ$ (Vertical field).
Q2. Which material has negative magnetic susceptibility?
(a) Paramagnetic (b) Diamagnetic (c) Ferromagnetic (d) None
Ans: (b) Diamagnetic.
Section B: Numericals (3 Marks)
Q3. At a certain location, the horizontal component of Earth's magnetic field is $0.3$ G and the angle of dip is $60^\circ$. Calculate the total magnetic field of the Earth.
Solution:
Given: $B_H = 0.3$ G, $\delta = 60^\circ$.
Formula: $B_H = B_E \cos \delta \Rightarrow B_E = \frac{B_H}{\cos \delta}$
$B_E = \frac{0.3}{\cos 60^\circ} = \frac{0.3}{0.5} = 0.6$ G.
Ans: 0.6 Gauss.
Section C: Conceptual (2 Marks)
Q4. Why do magnetic field lines form continuous closed loops?
Ans: Because magnetic monopoles (isolated North or South poles) do not exist. Field lines emerge from North and enter South outside, but return from South to North inside.
Q5. State Curie’s Law for paramagnetism.
Ans: The magnetic susceptibility ($\chi$) of a paramagnetic material is inversely proportional to its absolute temperature ($T$). i.e., $\chi = C/T$.
Mission 100 Physics Series
Next Chapter: Electromagnetic Induction (EMI)
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