Magnetic field and field lines

A magnetic field is the region of space around a magnet, or a current-carrying conductor, in which its magnetic effect can be detected — where a compass needle or another magnet feels a force. Like force and velocity, it is a vector quantity: at every point it has a magnitude (how strong the pull or twist is) and a direction. By convention, the direction of the field at a point is defined as the direction in which the north pole of a compass needle placed at that point would point.

Plotting the field. Two everyday methods reveal the field of a bar magnet. Placing a small plotting compass at several points around the magnet and marking the direction its needle takes, then joining those directions into smooth curves, traces the field lines point by point. Sprinkling iron filings on a sheet of paper laid over the magnet and tapping it gently does the same job faster — each filing becomes a tiny temporary magnet and aligns itself along the field direction at its location, so the filings bunch into visible curved chains.

The four rules. Every field-line diagram you draw or read must obey four facts, each traceable to what a field line represents. Field lines run outward from the north pole and inward into the south pole, everywhere outside the magnet. Inside the magnet the lines continue from S back to N, so every line is actually a closed loop — but for outside-the-magnet questions, remember simply N to S. The spacing between lines encodes the field's strength: lines drawn closer together mark a stronger field, and lines spread farther apart mark a weaker one. Near the poles, where the field is strongest, the lines are densest. No two field lines ever cross. A crossing point would need two different tangent directions at once, which would mean the field pointed two ways simultaneously at that spot — impossible, since a compass needle placed there can only settle in one direction. Field lines are continuous, unbroken curves that close on themselves, running from N, out through the space around the magnet, into S, and then through the body of the magnet back to N.

where: the proportionality is qualitative at this stage — no numerical value of field strength $B$ is required in Class 10, only the comparative statement that lines packed closer together mark the stronger region of the field. Where lines run parallel and evenly spaced, as they roughly do midway between the poles of a strong magnet, the field is called nearly uniform.

There is no formula for field strength at this level, so the reasoning that matters is why the four rules must be true rather than a calculation. Rule one — lines run N to S outside — follows directly from the compass definition: at every point the field line's tangent is the direction a free compass north pole would point, and a compass north pole is always pushed away from a nearby north pole and pulled toward a nearby south pole. Following that push-and-pull all the way from one pole of the magnet to the other traces a line that starts at N and ends at S. Rule two — spacing shows strength — follows because the same total "amount" of field spreads out from the pole. Near the pole the lines are squeezed into a small area, so they sit close together; far from the pole the same lines have spread over a much larger area, so they sit farther apart. Close spacing is simply a picture of a large amount of field packed into a small region. Rule three — no crossings — follows because the field has one true direction at each point, defined by where the compass needle settles. Two crossing lines would demand two different tangent directions at the same point, contradicting the single-valued definition of "the field direction here." Rule four — closed loops — follows from experiment (iron filings never simply stop or start at a random point in space) and reflects a deeper physical fact you will meet later: a magnet's field lines close on themselves because, unlike electric charge, isolated single magnetic poles have never been found.

Question: A student places a bar magnet under a sheet of paper, sprinkles iron filings, and taps the sheet. Filings gather into curved chains near both ends and lie almost straight and evenly spaced along the middle third of the magnet's length, roughly midway between the poles. Identify which pole is which, describe how the field strength varies along the magnet, and name the type of field seen in the middle region.

Step 1. The chains of filings running out of one end and curving around into the other end are the field lines. By the N-to-S rule, the end from which the lines emerge is the north pole, and the end into which they converge is the south pole.

Step 2. Close to both poles, the filings are noticeably crowded together; farther from the poles, along the sides, the chains spread apart. By the spacing rule, crowded lines mean a stronger field, so the field is strongest near each pole and weakens with distance from them.

Step 3. In the middle region, midway between the poles, the filings form straight, parallel, evenly spaced lines. Straight, parallel, and equally spaced lines are exactly the definition of a uniform field — same strength and same direction throughout that small region.

The filings reveal a north pole and a south pole joined by curved, non-crossing loops, a field that is strongest near the poles and weakest in between, and a small patch of nearly uniform field midway along the magnet.

• Treating field lines as physical threads that exist in space — they are a drawing convention for an invisible, continuous field, not real strings.
• Reversing the outside direction and saying lines run S to N — outside the magnet it is always N to S; only inside the magnet does the line continue S to N.
• Reading two field-line diagrams with the same spacing as showing different field strengths, or vice versa — spacing alone encodes strength; equal spacing means equal strength.
• Forgetting that a field line does not end at the south pole — it continues inside the magnet back to the north pole, forming one unbroken closed loop.

Ask the tutor: If a diagram shows field lines crossing, going the "wrong way," or stopping mid-air, ask the AI tutor to check it against these four rules and explain exactly which rule it breaks.