Class 12 Physics · Original EZT practice
Magnetism and Matter (Class 12 Chapter 5): summary and practice
Magnetism and Matter treats the bar magnet as a dipole: field lines, torque and potential energy in a field, the solenoid that imitates a magnet, Gauss's law for magnetism - and then the materials themselves, from diamagnetic to ferromagnetic. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 21 October 2026:
1. The bar magnet and its field lines
A bar magnet carries a north and a south pole that cannot be separated. Its field lines leave the north pole, close through the south pole and continue inside the magnet - closed loops with no beginning and no end, unlike electrostatic lines.
2. Dipole torque, energy and the solenoid
In a uniform field B a dipole moment m feels torque tau = m B sin(theta) but zero net force. Its potential energy is U = -m B cos(theta): most stable aligned with the field. A current loop or solenoid acts like a magnet with moment m = N I A, and the dipole formulas mirror the electrostatic ones with 1/4 pi epsilon0 swapped for mu0/4 pi.
3. Gauss's law for magnetism
The net magnetic flux through any closed surface is zero. There are no magnetic monopoles - every field line that enters a closed surface also leaves it, because magnetism always arrives in pole pairs.
4. Magnetisation, intensity and susceptibility
Inside a material the field splits into H (the magnetising intensity) and the material's own response M. Susceptibility chi = M/H measures how strongly the material responds, and relative permeability mu_r = 1 + chi ties B to H.
5. Dia, para and ferro materials
Diamagnetic materials are feebly repelled (chi small and negative), paramagnetic ones feebly attracted (chi small and positive), and ferromagnetic ones strongly attracted with domains, hysteresis and permanent magnets (chi large). Section 5.5.3 notes what makes a good permanent magnet: high coercivity and high retentivity.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Torque on a magnetic dipole
Choose the method: tau = m B sin(theta).
EZT practice question
A bar magnet of moment 0.5 J/T sits at 30 degrees to a uniform field of 0.2 T. Find the torque on it.
Show the worked solution
- tau = m B sin(theta).
- = 0.5 x 0.2 x sin 30 = 0.1 x 0.5.
Answer: tau = 0.05 N m.
Check: The torque is greatest at 90 degrees and zero when aligned - 30 degrees should give half the maximum, and it does.
Watch for this: The angle is between m and B - do not use the field-line direction at some random point.
Now try it yourself
Same magnet and field, now at 90 degrees. Maximum torque?
Check your answer
0.1 N m.
sin 90 = 1, so tau = 0.5 x 0.2 = 0.1 N m.
Potential energy of a dipole
Choose the method: U = -m B cos(theta).
EZT practice question
The same dipole (m = 0.5 J/T, B = 0.2 T) sits at 30 degrees to the field. Find its potential energy.
Show the worked solution
- U = -m B cos(theta).
- = -0.5 x 0.2 x cos 30 = -0.1 x 0.866.
Answer: U = -0.0866 J (approximately).
Check: Negative energy means the field has already pulled the dipole toward alignment - the aligned state at 0 degrees is the deepest at -0.1 J.
Watch for this: Do not drop the minus sign - U = -mB at alignment is the stable equilibrium, not +mB.
Now try it yourself
Same dipole at 0 degrees. Potential energy?
Check your answer
-0.1 J.
cos 0 = 1, so U = -mB = -0.1 J, the stable equilibrium.
Gauss's law for magnetism
Choose the method: Net magnetic flux through any closed surface is zero.
EZT practice question
A closed surface completely surrounds the north pole end of a bar magnet. What is the net magnetic flux through it?
Show the worked solution
- Magnetic field lines form closed loops with no free poles.
- Every line entering the surface also leaves it.
Answer: Zero - the net flux through any closed surface is always zero.
Check: This is exactly the statement that magnetic monopoles do not exist; contrast with electrostatics, where a closed surface around a charge gives q/epsilon0.
Watch for this: Do not count the lines that visibly enter the surface near the pole and forget the same lines leaving elsewhere.
Now try it yourself
A closed surface encloses a whole bar magnet. Net flux?
Check your answer
Zero.
Both poles are inside; every loop that leaves returns, so the net flux is zero as always.
Magnetic moment of a solenoid
Choose the method: m = N I A.
EZT practice question
A solenoid has 200 turns, each of area 2 x 10^-4 m^2, and carries 5 A. Find its equivalent magnetic moment.
Show the worked solution
- m = N I A.
- = 200 x 5 x 2 x 10^-4.
Answer: m = 0.2 J/T (0.2 A m^2).
Check: More turns, more current or more area all scale the moment linearly - double any one and m doubles.
Watch for this: Keep the units straight: m in A m^2 (equivalently J/T), not in tesla.
Now try it yourself
Same solenoid at 10 A. Magnetic moment?
Check your answer
0.4 J/T.
Doubling the current doubles m: 200 x 10 x 2 x 10^-4 = 0.4.
From susceptibility to permeability
Choose the method: mu_r = 1 + chi.
EZT practice question
A material has magnetic susceptibility chi = 0.0002. Find its relative permeability and classify it.
Show the worked solution
- mu_r = 1 + chi.
- = 1 + 0.0002.
- chi is small and positive.
Answer: mu_r = 1.0002 - slightly above 1, so the material is paramagnetic.
Check: Paramagnetic materials sit just above mu_r = 1; diamagnetic ones just below; ferromagnetic ones far above.
Watch for this: A small POSITIVE chi is paramagnetic - only a negative chi is diamagnetic.
Now try it yourself
A material with chi = -0.00002. Relative permeability and type?
Check your answer
0.99998, diamagnetic.
1 + (-0.00002) = 0.99998, just below 1.
Identify the magnetic material
Choose the method: Match the observed behaviour to dia, para or ferro.
EZT practice question
A rod placed in a non-uniform magnetic field moves feebly from the strong part of the field toward the weak part. Classify the material.
Show the worked solution
- Repelled by the field = pushed toward the weaker region.
- That is the signature of a negative susceptibility.
Answer: Diamagnetic.
Check: Paramagnetic rods drift feebly toward the STRONG region; ferromagnetic ones snap toward it.
Watch for this: Feeble repulsion is not no magnetism - every material responds; the question is which way and how strongly.
Now try it yourself
A rod is strongly pulled into the field and keeps its magnetisation after removal. Type?
Check your answer
Ferromagnetic.
Strong attraction plus retained magnetisation (hysteresis) is the ferromagnetic signature.
Try a mixed set
Choose a method or explanation before opening each answer.
1. Torque on a dipole?
Show answer and reason
tau = m B sin(theta).
Maximum at 90 degrees, zero when aligned.
2. Dipole potential energy?
Show answer and reason
U = -m B cos(theta).
Aligned with the field is the stable minimum.
3. Gauss's law for magnetism?
Show answer and reason
Net flux through a closed surface is zero.
No magnetic monopoles exist.
4. Susceptibility vs permeability?
Show answer and reason
mu_r = 1 + chi.
Chi negative: dia; small positive: para; large: ferro.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- A dipole of moment 0.5 J/T in a 0.2 T field at 90 degrees. Find the maximum torque.
- The same dipole aligned with the field (0 degrees). Find its potential energy.
- A material with chi = -0.00002. Find its relative permeability and name its type.
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Questions about this practice page
- What is the difference between diamagnetic, paramagnetic and ferromagnetic materials?
- Diamagnetic materials are feebly repelled by a magnet (chi small and negative), paramagnetic ones are feebly attracted (chi small and positive), and ferromagnetic ones are strongly attracted and can stay magnetised - domains, hysteresis and permanent magnets live here.
- Why do magnetic field lines form closed loops?
- Because there are no magnetic monopoles. A line that leaves the north pole re-enters at the south pole and continues through the magnet, so the net flux through any closed surface is zero - Gauss's law for magnetism.
- Is there anything after section 5.5 in this chapter?
- No. In the current rationalised reprint the chapter ends at 5.5, Magnetic Properties of Materials, which includes the permanent-magnet requirements of 5.5.3. Older books carried later sections that the rationalised edition has moved or removed.
- What is the difference between B and H?
- H is the magnetising intensity produced by external currents; B is the total field inside the material, which adds the material's own magnetisation response. They are linked by the permeability of the material.
- Are these the NCERT exercise questions for Magnetism and Matter (Class 12)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.