Magnetic field due to a straight conductor

Oersted's experiment. Run a wire over a compass, parallel to the needle's rest direction, and switch on the current — the needle swings. Switch off, it returns to north. Reverse the current's direction, it swings the other way. None of this happens with the current off, so the current itself, not the wire, is the source of the field. This is the founding experiment of electromagnetism: electricity and magnetism are not separate phenomena but two faces of one thing.

The shape of the field. Push a vertical wire through a hole in a horizontal cardboard sheet, sprinkle iron filings on the sheet, and pass a strong current through the wire. Tap the board gently and the filings snap into a pattern of concentric circles, all centred on the wire, lying flat in the plane of the cardboard — that is, in a plane perpendicular to the wire. Place a small compass anywhere on one of these circles and its needle aligns along the tangent to that circle, never pointing toward or away from the wire. This confirms the field lines genuinely loop around the wire rather than radiating outward from it like spokes.

How strength depends on current and distance (qualitative only). Three trends, all confirmed by watching compass deflection or the tightness of the filings pattern:

• Move the compass closer to the wire and the deflection grows — the field is stronger near the wire.
• Move it farther away and the deflection shrinks — the field gets weaker with distance, though it never quite vanishes at any finite distance.
• Increase the current (say, by adding more cells) and the deflection grows at every fixed point — the field strengthens with current.

The circles nearest the wire in an iron-filings picture are drawn tightly packed; farther out, they space apart — a visual shorthand for "stronger near, weaker far," even though no numeric field strength is ever calculated at this level.

There is no formula to derive here — the syllabus deliberately keeps the straight-wire field qualitative — but the reasoning behind the three trends is worth spelling out, because exam questions often test whether you can reconstruct it rather than just recite it. Start from Oersted's core fact: current is the source of the field, not the wire's material. A copper wire and a steel wire carrying the same current in the same shape produce the same field pattern, which rules out the wire's own magnetism as the cause — it must be the moving charge itself. Next, why circles and not radial lines. A compass needle at any point around the wire settles along the tangent to a circle centred on the wire, never pointing toward or away from it. If the field pointed radially (in or out), the needle would align along a line straight to the wire; it does not — it always sits perpendicular to that radial direction. The only pattern consistent with "always tangential, always centred on the wire" is a family of concentric circles. Why the field is stronger near the wire: the iron filings and compass deflection both weaken smoothly as you move outward, with no formula needed to see the trend — the same current is "spreading its influence" over a larger circle at greater distance, so the effect per unit length of that circle is diluted. This is why the diagrammatic circles are drawn closer together near the wire (denser field) and farther apart away from it (sparser field) — density of lines is the standard way to show field strength changing without writing an equation. Why reversing the current reverses the sense: the compass deflects in the opposite direction the instant the current direction is reversed, showing the field's rotational sense (clockwise vs anticlockwise, viewed along the current) is tied directly to which way the charge moves. The shape — still concentric circles — does not change, only which way they "curl." The precise rule connecting current direction to circulation direction is the right-hand thumb rule, developed in the next article; here it is enough to know that reversing current flips the sense.

Question: A long straight vertical wire carries a current flowing upward. A compass is placed due east of the wire, at the same height, and points roughly north when the current flows. (a) Is the field circling the wire clockwise or anticlockwise, as seen from above with the current coming toward the viewer? (b) If the current is doubled without moving the compass, what happens to the deflection? (c) If the compass is instead moved twice as far east (current unchanged), what happens to the deflection compared to its original position?

Step 1. The field lines around any straight current-carrying wire are concentric circles centred on the wire, lying in planes perpendicular to it — this is true regardless of current strength or the compass's distance.

Step 2. At the point east of the wire, the tangent to the circle through that point points north (this matches the given information — the field there points north), so the circulation, viewed from above with current coming up toward the viewer, is anticlockwise.

Step 3. Since field strength increases with current at a fixed distance, doubling the current while keeping the compass at the same spot makes the field there stronger, so the compass deflection increases.

Step 4. Since field strength decreases with distance at fixed current, moving the compass twice as far from the wire (current unchanged) puts it in a weaker part of the field, so the deflection decreases compared to the original position.

Final answer: the field circles anticlockwise (viewed from above); doubling the current increases the deflection; doubling the distance decreases the deflection.

Competitive stretch

If a question instead compares two different wires — say wire P carrying twice the current of wire Q — the same two trends combine: at matching distances from each wire, P's field is stronger (more current, same distance); and for either wire alone, moving farther away always weakens its own field (same current, more distance). Keep the two variables — current and distance — separate in your reasoning; never let "P has more current" bleed into a claim about distance, or vice versa.

• Drawing the field lines around a straight wire as straight radial lines shooting outward — they are circles wrapped around the wire, and a compass placed near the wire always points along the tangent to its circle, never toward or away from the wire.
• Assuming the field disappears at some fixed "edge" distance — it only gets weaker and weaker with distance, never becoming exactly zero at any finite distance from the wire.
• Trying to plug numbers into $B = \dfrac{\mu_0 I}{2\pi r}$ for a Class 10 answer — this formula and the Biot–Savart law are explicitly outside the CBSE Class 10 syllabus; describe trends in words only ("field strength increases with current," "decreases with distance").
• Forgetting that reversing the current reverses the circulation sense (clockwise to anticlockwise or vice versa) even though the circular shape of the field lines itself does not change.

Ask the tutor: If you are unsure whether the field circles clockwise or anticlockwise for a given current direction, sketch it and ask the AI tutor to check your reasoning against the right-hand thumb rule.