Two magnetic field lines produced by the same source

Correct — A, never intersect. A magnetic field line is drawn so that its tangent at every point gives the direction a compass needle would settle into there. Two lines crossing would mean the field had two different directions at the crossing point, and a compass placed there would have to point two ways at once. Since the field at any point has one definite direction, the lines can never meet.

• (b)can originate from same point — Lines starting from a single common point would be crossing at that point, which brings back the same impossibility — two field directions at one place.
• (c)can terminate at same point — Ending together is the same defect read backwards. Field lines run in closed loops, out of the north pole through the surrounding space and back in at the south pole, continuing through the magnet itself.
• (d)can intersect depending on situation — There is no situation in which they cross. The rule follows from the field being a single-valued vector at each point, not from the shape of any particular magnet.

Field lines are a bookkeeping device for a vector field. Their direction at a point records the direction of the field there, and how closely they are packed records its strength. Both pieces of information would break down if two lines were allowed to cross, so the no-crossing rule is built into the drawing convention rather than being an experimental accident.

The stem's phrase 'produced by the same source' is there to close the obvious loophole a student reaches for, which is that two magnets brought near each other might make lines cross. They still cannot. When two sources overlap, their fields add as vectors and a single new set of non-crossing lines results, sometimes with a neutral point where the field cancels and no line passes at all. Electric field lines obey the same rule for the same reason.

• The tangent to a magnetic field line at any point gives the direction of the field, so two lines through one point would give it two directions.
• Magnetic field lines are closed loops — outside a bar magnet they run north to south, inside the magnet they run south to north.
• Crowded lines mean a strong field, which is why they bunch near the poles of a bar magnet.
• Where two fields cancel exactly, a neutral point forms and no field line passes through it.
• Electric field lines also never cross, but unlike magnetic lines they begin on positive charges and end on negative ones instead of closing on themselves.

• Thinking two different magnets can produce crossing lines.
• Drawing field lines that stop in mid-air outside a magnet instead of closing through it.
• Confusing a neutral point, where no line passes, with a point where lines cross.

A one-line property recall, usually phrased so that three options are restatements of the forbidden case.

• practice — not a real PYQ

  Magnetic field lines inside a bar magnet are directed from

  • (a)north pole to south pole
  • (b)south pole to north pole
  • (c)the middle outwards to both poles
  • (d)there are no field lines inside a magnet

  Answer(b) south pole to north pole — the lines close on themselves, running north to south outside the magnet and south to north within it.

• practice — not a real PYQ

  The relative closeness of magnetic field lines in a region indicates

  • (a)the direction of the field
  • (b)the strength of the field
  • (c)the polarity of the nearest magnet
  • (d)the temperature of the region

  Answer(b) the strength of the field — closely packed lines mean a strong field, which is why they crowd near the poles.