Magnetism and Matter — Complete Formula

Bar Magnet as Equivalent Solenoid

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Magnetic Moment	[M = NI A]	[M] = magnetic moment, [N] = turns, [I] = current, [A] = area	A·m²	Solenoid equivalence ⭐

💡 Memory Hint:
Bar magnet behaves like a current loop

Position	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Axial Line	[B = \dfrac{\mu_0}{4\pi} \dfrac{2M}{r^3}]	[r] = distance	T	Stronger field ⭐
Equatorial Line	[B = \dfrac{\mu_0}{4\pi} \dfrac{M}{r^3}]	—	T	Half of axial ⚠️

💡 Memory Hint:
Axial field = 2 × equatorial field

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Torque	[\tau = MB\sin\theta]	[\theta] = angle with field	N·m	Rotates magnet ⭐
Potential Energy	[U = -MB\cos\theta]	—	J	Stable at minimum energy ⭐

💡 Memory Hint:
Magnet tries to align with field

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Nature	Closed loops	—	—	No monopoles ⭐

💡 Memory Hint:
Field lines always form closed loops

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Horizontal Component	[B_H = B\cos\theta]	[\theta] = dip angle	T	Important ⭐
Vertical Component	[B_V = B\sin\theta]	—	T	Downward in N hemisphere
Resultant Field	[B = \sqrt{B_H^2 + B_V^2}]	—	T	Vector addition

💡 Memory Hint:
Resolve Earth’s field into horizontal + vertical

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Magnetization	[M = \dfrac{m}{V}]	[m] = magnetic moment, [V] = volume	A/m	Magnetic strength ⭐
Magnetic Intensity	[H = \dfrac{B}{\mu_0} – M]	[H] = magnetic field intensity	A/m	Important relation ⭐
Susceptibility	[\chi = \dfrac{M}{H}]	[\chi] = susceptibility	—	Material property ⭐

💡 Memory Hint:
Susceptibility → response to field

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Fundamental Relation	[B = \mu_0 (H + M)]	—	T	Most important ⭐
Using Susceptibility	[B = \mu_0 (1 + \chi)H]	—	T	Simplified form
Permeability	[\mu = \mu_0 (1 + \chi)]	[\mu] = permeability	H/m	Material property

💡 Memory Hint:
[B] depends on both external field + material response

Type	Property	Susceptibility [\chi]	Key Notes
Diamagnetic	Weak repulsion	[\chi < 0]	e.g., copper ⭐
Paramagnetic	Weak attraction	[\chi > 0]	e.g., aluminium
Ferromagnetic	Strong attraction	[\chi \gg 1]	e.g., iron ⭐

💡 Memory Hint:

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Curie Law	[\chi = \dfrac{C}{T}]	[C] = Curie constant, [T] = temperature	—	For paramagnetic ⭐

💡 Memory Hint:
Temperature ↑ → susceptibility ↓

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Energy Loss	Area of B–H loop	—	—	Important ⭐
Retentivity	Residual magnetism	—	—	Memory of material
Coercivity	Reverse field needed	—	—	Demagnetization

💡 Memory Hint:
Loop area = energy loss

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