NDA (I) 2018 General Ability Test · Question 55 of 150

Correct — A, Zero. A bar magnet is a magnetic dipole — it carries a north pole and a south pole of equal strength, and the two are inseparable. In a uniform field the field has the same strength and the same direction everywhere, so it pushes the north pole one way with a certain force and pulls the south pole the opposite way with a force of exactly the same size. The two cancel and the net force on the magnet is zero. The magnet does not stay still, though: the two equal and opposite forces act at different points, so they form a couple that turns the magnet until it lines up with the field. Force zero, torque generally not zero.

• (b)Depends upon length of the magnet — The length affects the torque, because the turning effect depends on how far apart the two poles are, but it cannot affect the net force. Whatever the separation, the pole strengths remain equal and opposite, so the two forces still cancel exactly.
• (c)Never zero — This is the opposite of the truth in a uniform field. A magnet does feel a net force in a non-uniform field — that is why a magnet attracts an iron nail, and why the stronger end of the field wins — but the question has specified a uniform field precisely to remove that.
• (d)Depends upon temperature — Temperature does weaken a magnet, and above its Curie temperature a ferromagnet loses its magnetism altogether. But that only changes the size of the two pole forces together; they remain equal and opposite, so their sum stays zero.

A uniform magnetic field is one whose strength and direction are the same at every point in the region considered — the field inside a long current-carrying solenoid is the standard example. A bar magnet placed in such a field behaves as a magnetic dipole of moment equal to the pole strength times the separation of the poles. The net force on that dipole is zero, while the torque on it is the magnetic moment times the field strength times the sine of the angle between them. The torque therefore vanishes only when the magnet is already aligned with the field.

The item is testing whether a candidate separates force from torque, and the everyday intuition works against the right answer. A compass needle placed in the Earth's field swings round and settles pointing north, and it is tempting to describe that as the field 'pulling' the needle. It is not pulling it anywhere — the needle's centre stays exactly where it was. The field only turns it. Any time a question specifies a uniform field, expect the answer for net force on a dipole to be zero and expect the physics to be about the turning effect. Change the wording to a non-uniform field and the answer flips, because then the two poles sit in different field strengths and the cancellation is no longer exact.

• Magnetic poles always occur in pairs; breaking a bar magnet in two produces two complete magnets, not an isolated pole.
• In a uniform field the net force on a magnetic dipole is zero but the torque generally is not.
• The torque is largest when the magnet lies at right angles to the field and zero when it is aligned with it.
• In a non-uniform field a magnet does experience a net force, which is why magnets attract nearby iron objects.
• Above the Curie temperature a ferromagnetic material loses its permanent magnetism.

• Confusing the turning effect of a field with a net pull on the magnet.
• Carrying over the non-uniform-field intuition of a magnet attracting iron into a question that says uniform.
• Thinking a longer magnet must feel a larger force, when length affects only the torque.

Asked directly, as here, or through the solenoid — which behaves like a bar magnet and produces the uniform field in the first place.

• practice — not a real PYQ

  A bar magnet placed in a uniform magnetic field at an angle to the field will

  • (a)move along the field without rotating
  • (b)rotate until it aligns with the field, without any net translation
  • (c)move against the field
  • (d)neither rotate nor move

  Answer(b) rotate until it aligns with the field, without any net translation — the forces on the two poles cancel but form a couple.

• practice — not a real PYQ

  A bar magnet is cut into two equal halves across its middle. Each half will be

  • (a)a north pole only
  • (b)a south pole only
  • (c)a complete magnet with both poles
  • (d)non-magnetic

  Answer(c) a complete magnet with both poles — magnetic poles cannot be isolated.