Q.(a) What happens if a bar magnet is cut into two pieces:

(a) Cutting a bar magnet

Concept: Each piece of a broken magnet becomes a complete magnet with its own north and south poles — magnetic poles always occur in pairs.

• Transverse cut (perpendicular to length): You get two shorter bar magnets, each with a north and south pole. …

(a) Cutting a bar magnet

Concept: A bar magnet’s magnetism comes from aligned atomic magnetic moments. Cutting the magnet does not destroy these moments — it simply separates the material into two pieces, each of which still has aligned moments. So each piece becomes a complete magnet with its own north and south pole.

1. Cut transverse to the length (perpendicular to the magnet’s long axis)

You get two shorter bar magnets. The original north pole remains a north pole on its piece; the original south pole remains a south pole on its piece. The cut ends become opposite poles: the end that was near the original north becomes a south pole, and the end near the original south becomes a north pole.

2. Cut along the length (parallel to the long axis)

You get two thinner bar magnets. Each has a north pole and a south pole at its ends. The original north pole splits into two north poles (one on each piece), and the original south pole splits into two south poles.

(b) Needle vs. nail — why the difference?

Concept: A force on a magnetic dipole in a magnetic field depends on the gradient (non‑uniformity) of the field. Torque depends only on the field itself.

1. Magnetised needle in a uniform field

The needle is a dipole. In a perfectly uniform field, the forces on its north and south poles are equal in magnitude but opposite in direction — they cancel exactly. So net force is zero. But the two forces form a couple, producing a torque that aligns the needle with the field.

2. Iron nail near a bar magnet

The bar magnet’s field is non‑uniform — it weakens with distance. The nail is not permanently magnetised; it becomes an induced magnet. The near end of the nail acquires opposite polarity to the bar magnet’s pole, so there is an attractive force. Because the field is stronger at the near end than at the far end, the forces on the induced north and south poles of the nail do not cancel — there is a net force toward the bar magnet. Additionally, the nail experiences a torque trying to align it with the field.

(c) Must every magnetic configuration have a north and a south pole?

Concept: The magnetic field lines are always closed loops. For a finite magnet, the field emerges from one region (north pole) and enters another (south pole). But for a closed‑loop geometry, the field can circulate without any “starting” or “ending” point.

1. General rule

In classical electromagnetism, magnetic monopoles do not exist. So any finite piece of magnetic material will have both a north and a south pole — the field lines must leave from somewhere and return somewhere else.

2. The toroid exception

A toroid is a coil wound into a doughnut shape. Its magnetic field is entirely confined within the core and circulates in closed loops around the toroid. There is no region where field lines emerge or enter — no poles at all. So the answer is no: a toroid has no north or south pole.

(d) Identifying which bar is magnetised

Concept: A magnet attracts unmagnetised iron, but it can also repel another magnet if like poles are brought together. Attraction alone is ambiguous — an unmagnetised iron bar will also be attracted to a magnet. Only repulsion is a sure test of magnetism.

Procedure using only the two bars:

1. Test for repulsion

   Take bar A and bring one of its ends near one end of bar B. If they repel, then both bars are magnetised (repulsion only occurs between like poles). If they attract, you cannot conclude yet — it could be a magnet attracting iron, or two magnets attracting with opposite poles.

2. If attraction is observed

   Rotate bar A by 180° and bring the same end of A near the same end of B again. …

Here is a clear, concept-first solution for each part, using the Principle of Magnetic Poles and Domain Theory.

(a) Cutting a Bar Magnet

Method: Magnetic Monopole Non-existence & Domain Alignment

Concept: Magnetic poles always exist in pairs (North and South). You cannot isolate a single pole. Cutting a magnet simply creates two new smaller magnets, each with its own N and S pole.

(i) Cut transverse to its length (perpendicular to the axis):

• What happens: You get two complete, smaller bar magnets.
• Why: The cut separates the original North end from the South end. The broken ends become opposite poles.
• Result: The piece that had the original North pole now has a South pole at the cut end. The piece that had the original South pole now has a North pole at the cut end.

(ii) Cut along its length (parallel to the axis):

• What happens: You get two thin, long bar magnets.
• Why: Each half contains a full set of aligned domains from North to South.
• Result: Each piece is a weaker magnet, but still has a North pole at one end and a South pole at the other.

Key Result: In both cases, you never get an isolated North or South pole. You always get two new complete magnets.

(b) Torque vs. Force on Magnetic Objects

Method: Uniform vs. Non-Uniform Field Analysis

Concept: A uniform magnetic field exerts equal and opposite forces on the N and S poles of a magnet, causing a torque (turning effect) but zero net force. A non-uniform field exerts unequal forces on the poles, producing a net force (attraction or repulsion).

Why the nail is attracted:

• The nail is a temporary magnet (induced magnetism).
• The end of the nail closer to the bar magnet becomes the opposite pole.
• Because the field is stronger near the bar magnet, the attractive force on the near pole is greater than the repulsive force on the far pole.
• Result: A net force pulls the nail toward the magnet.

(c) Must Every Magnetic Configuration Have a North and South Pole?

Method: Gauss's Law for Magnetism & Closed Loop Fields

Answer: No, not every configuration must have distinct North and South poles.

• Gauss's Law for Magnetism: $\oint \vec{B} \cdot d\vec{A} = 0$. This means magnetic field lines always form closed loops. There are no magnetic monopoles.
• Bar magnet: Field lines emerge from the North pole and enter the South pole outside the magnet, but they continue inside the magnet from South to North, forming a closed loop. This gives the appearance of two distinct poles.
• Toroid (doughnut-shaped coil):
  • The magnetic field is entirely confined within the core of the toroid.
  • The field lines are circular and closed within the toroid itself.
  • There is no external field. Therefore, there is no point where field lines "emerge" or "enter" the outside space.
  • Conclusion: A toroid has no identifiable North or South pole. It is a pole-less magnetic configuration.

Key Result: A toroid is a counterexample to the idea that every magnet must have two poles.

(d) Identifying the Magnetised Bar (Using Only the Two Bars)

Method: Attraction vs. Repulsion Test

Concept: A magnet attracts an unmagnetised iron bar. However, two magnets can either attract or repel each other depending on orientation. Repulsion is the only sure test of magnetism. …

Here are the common mistakes students make on this topic, broken down by sub-question, with the correct concept and exam-smart avoidance strategies.

(a) Cutting a Bar Magnet

Common Mistake 1: Thinking the poles get separated.

• The Error: Students often say that cutting a magnet transversely gives a "north piece" and a "south piece."
• The Correct Concept: Every piece of a magnet, no matter how small, is a complete dipole. You cannot isolate a single pole.
• How to Avoid: Memorise the rule: Fragmentation always produces two new poles at the cut surface. The new poles are opposite to the pole at the other end of that piece.

Common Mistake 2: Confusing the results of transverse vs. longitudinal cuts.

• The Error: Thinking both cuts produce the same result (two small magnets).
• The Correct Concept:
  • Transverse cut (perpendicular to length): You get two separate, weaker bar magnets. Each has its own North and South pole.
  • Longitudinal cut (along the length): You get two long, thin magnets. Each still has a North and South pole at its ends.
• How to Avoid: Draw a diagram. For the transverse cut, draw a line across the middle. For the longitudinal cut, draw a line down the middle. Label the poles on each new piece.

The Exam-Ready Answer:

• (i) Transverse: Two complete bar magnets, each with a North and South pole. The pole at the cut end of the left piece is opposite to the pole at the cut end of the right piece.
• (ii) Along its length: Two complete bar magnets, each with a North and South pole at their respective ends. The magnetic strength of each is reduced.

(b) Torque vs. Force on a Magnet

Common Mistake 3: Forgetting the condition for a net force.

• The Error: Assuming any magnet near another magnet always experiences a net force.
• The Correct Concept:
  • Uniform Field (Magnetised Needle): The forces on the North and South poles are equal in magnitude but opposite in direction. They form a couple (producing torque) but cancel out as a net force ($F_{net} = 0$).
  • Non-Uniform Field (Iron Nail near Bar Magnet): The field is stronger near the magnet's pole. The force on the nail's induced pole closer to the magnet is stronger than the force on the far pole. This imbalance creates a net attractive force.
• How to Avoid: Always ask: Is the magnetic field uniform or non-uniform? If uniform, only torque. If non-uniform, both torque and net force.

The Exam-Ready Answer:

The needle is in a uniform field (torque only). The nail is in a non-uniform field (the field strength decreases with distance from the bar magnet), so the forces on its induced poles are unequal, producing a net force.

(c) Necessity of Poles

Common Mistake 4: Assuming all magnetic fields come from dipoles.

• The Error: Stating that every magnetic configuration must have a North and South pole.
• The Correct Concept: This is true for bar magnets, solenoids, and the Earth. However, a toroid (a solenoid bent into a ring) has a magnetic field that is entirely confined within its core. There are no free poles. …