Q.Many of the diagrams given in Fig. 5.6 show magnetic field lines (thick lines in the figure) wrongly. Point out what is wrong with them. Some of them may describe electrostatic field lines correctly. Point out which ones.

The key idea is that magnetic field lines form continuous closed loops — they never start or end at a point (no monopoles), and they cannot cross in empty space.

Step 1 — Check for monopoles: In (a), lines radiate outward from a single point. This is impossible for a magnetic field — it would require a magnetic monopole. This diagram is wrong for magnetism but would be correct for an electrostatic field (a point charge).

Step 2 — Check for crossing lines: In (b), two families of straight lines cross each other. Field lines cannot intersect in empty space because the field direction would be ambiguous. This is wrong for both magnetic and electrostatic fields.

Step 3 — Check for continuity and confinement:

• (c) shows closed concentric loops confined to a toroid — correct for a toroidal magnetic field.
• (d) shows solenoid field lines continuing perfectly straight outside — wrong; they should spread out and loop back.
• (e) shows field lines inside the magnet, forming closed loops — correct.
• (f) shows field lines bulging symmetrically from two plates — this is an electrostatic field pattern (parallel plates), not magnetic.
• (g) shows a closed magnetic circuit with N and S poles — correct for a ring magnet.

The key idea is that magnetic field lines are fundamentally different from electrostatic field lines. Electrostatic field lines start on positive charges and end on negative charges — they can diverge from a point. Magnetic field lines, however, have no sources or sinks; they always form continuous closed loops. This follows from Gauss's law for magnetism: $\nabla \cdot \mathbf{B} = 0$, which says magnetic monopoles don't exist.

Let's examine each diagram:

1. Diagram (a) — Lines radiating outward from a single point. This is impossible for a magnetic field because it would require a magnetic monopole (a north pole without a south pole). Magnetic field lines must form closed loops. However, this pattern is correct for an electrostatic field — it describes the field of a positive point charge. The dashed vertical line with a knob at top likely represents a charged rod, making this an electrostatic field line diagram.

2. Diagram (b) — Two families of straight lines crossing each other in an X pattern. Field lines can never cross. At the crossing point, the field would have two different directions simultaneously, which is physically impossible. The curl arrows at the sides suggest some attempt at showing circulation, but the crossing lines are the fundamental error. This is wrong for both magnetic and electrostatic fields.

3. Diagram (c) — Concentric closed circular loops confined within a dashed boundary. This is a correct representation of a toroidal magnetic field. The field lines form closed loops around the torus, never leaving the region. The arrowheads show consistent direction around each loop. This is correct for a magnetic field but would be wrong for an electrostatic field (which cannot form closed loops).

4. Diagram (d) — A solenoid with straight field lines continuing perfectly straight out both ends. The error is subtle but important: magnetic field lines from a solenoid do not continue straight indefinitely. They spread out and loop back around to form closed paths. The field lines emerging from one end of the solenoid must curve around and re-enter the other end. Showing them as straight lines that never close violates the closed-loop nature of magnetic fields.

5. Diagram (e) — A bar magnet with field lines shown both outside and inside the magnet, forming closed loops. This is correct. The lines emerge from the north pole, curve around outside, enter the south pole, and continue through the interior of the magnet back to the north pole. Showing the internal field lines is important — many students forget that the field exists inside the magnet too.

6. Diagram (f) — Two short horizontal plates with field lines bulging outward symmetrically above and below. This pattern describes the electrostatic field of a parallel-plate capacitor (with fringing fields at the edges). For a magnetic field, this would be wrong because the lines don't form closed loops — they appear to start and end on the plates. But for an electrostatic field, this is correct: field lines start on positive charges and end on negative charges.

7. Diagram (g) — A rounded-rectangle closed loop (a bar magnet bent into a ring) with N and S poles at the top-centre, and field lines forming a closed magnetic circuit. This is correct. The field lines form continuous closed paths through the magnetic material and the gap. This is essentially a toroidal magnet with a small air gap.

Method: Validating a Magnetic (or Electrostatic) Field-Line Diagram

Use this checklist whenever you are asked to judge whether a drawn set of field lines correctly represents a magnetic field, an electrostatic field, or neither.

Steps

Step 1: Check for a source or sink (the monopole test)

Magnetic field lines can never start or end at a point in space — they must form continuous closed loops. This follows from $\nabla\cdot\vec{B}=0$ (no magnetic monopoles). If lines radiate outward from, or converge into, a single point, the diagram is wrong for a magnetic field.

Step 2: Check for crossing lines

Field lines of any kind — magnetic or electric — can never intersect. At a crossing point the field direction would be ambiguous, which is physically impossible. A diagram with crossing lines is wrong regardless of which field it claims to show.

Step 3: Check continuity through the source region

For a magnet, field lines must continue through the material (south to north inside) to close the loop that runs north to south outside. A diagram that shows lines only outside the object, or that lets them stop abruptly at a boundary without closing, is wrong.

Step 4: If it fails as magnetic, re-test it as electrostatic

Diagrams that radiate from a point, or terminate cleanly on a surface (like capacitor plates), often ARE valid for electrostatic fields, since electric field lines legitimately begin on positive charge and end on negative charge. Re-check the same diagram against the electrostatic rules (start/end on charges, never cross) before ruling it out completely.

Step 5 (Applying to this problem): State a verdict per sub-diagram

Apply Steps 1–4 to every labelled panel individually, and give each one an independent verdict — correct-for-magnetic / wrong-for-magnetic-but-correct-for-electrostatic / wrong-for-both. Never assume all panels in a figure share the same verdict.