“Di runs away, para follows, ferro clings”
The three kinds of material
Diamagnetic is weakly repelled, paramagnetic weakly attracted, ferromagnetic strongly attracted and able to stay magnetised.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Magnetism and Matter formulas
A short, mostly theoretical chapter that reliably supplies one or two marks. The bar magnet formulas mirror the electric dipole exactly, and the three kinds of magnetic material are a classification question you can answer in a table.
16 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Bar magnet as a dipole
| What | Formula | Symbols and notes |
|---|---|---|
| Magnetic dipole moment | m = pole strength × 2l | unit A m² |
| Axial field | B = (μ₀/4π)(2m/r³) | on the axis, far from the magnet |
| Equatorial field | B = (μ₀/4π)(m/r³) | half the axial value, opposite direction |
| Torque | τ = mB sinθ | the compass needle lines up with the field |
| Potential energy | U = −mB cosθ | minimum when aligned |
| Time period of oscillation | T = 2π√(I/mB) | I is the moment of inertia of the magnet |
Earth's magnetism
| What | Formula | Symbols and notes |
|---|---|---|
| Components | BH = B cosδ, BV = B sinδ | δ is the angle of dip |
| Angle of dip | tanδ = BV/BH | zero at the magnetic equator, 90° at the poles |
| Declination | the angle between geographic and magnetic north | varies with place and slowly with time |
Materials
| What | Formula | Symbols and notes |
|---|---|---|
| Magnetic intensity | H = B/μ₀ − M | M is the magnetisation |
| Susceptibility | χ = M/H | a pure number |
| Permeability | μ = μ₀(1 + χ) | relative permeability μr = 1 + χ |
| Diamagnetic | χ small and negative | weakly repelled, for example bismuth, copper, water |
| Paramagnetic | χ small and positive | weakly attracted, for example aluminium, oxygen |
| Ferromagnetic | χ large and positive | strongly attracted, for example iron, cobalt, nickel |
| Curie's law | χ ∝ 1/T | heating destroys the alignment |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Same shape as the electric dipole”
Bar magnet fields
Axial 2m over r cubed, equatorial m over r cubed, exactly as for an electric dipole with p replaced by m.
“Dip is zero at the equator”
Earth's magnetic field
A dip needle lies flat at the magnetic equator and stands vertical at the magnetic poles.
Where marks go
The mistakes that cost the most.
- Saying magnetic field lines start at the north pole and stop at the south. They are closed loops and continue inside the magnet.
- Believing a single magnetic pole can exist. Cutting a magnet in half gives two complete magnets.
- Mixing up dip and declination. Dip is measured vertically, declination horizontally.
- Forgetting that heating a ferromagnet past its Curie temperature makes it paramagnetic.
- Using B where H is asked in a magnetisation question; they have different units.
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