CortexHSC

Year 11 Physics · Electricity and magnetism · Magnetism · 13 min read

Magnetic fields

A magnetic field is the region around a magnet or a current where a magnetic force acts. In Year 11 Physics you draw these fields with field lines, find their direction with the right-hand grip rule, and calculate their strength for two shapes of current: a long straight wire and a solenoid (a coil).

This guide covers field lines, the bar magnet, wires and loops, the dot and cross symbols for 'out of' and 'into' the page, B = μ0I ÷ 2πr, solenoids, and what makes an electromagnet stronger. Then come the common mistakes, a quick quiz and a full worked example.

What you need to know

The equations you will use:

B = μ0I ÷ 2πrField strength (tesla, T) at distance r (metres) from a long straight wire carrying current I (amperes).
B = μ0NI ÷ LUniform field inside a solenoid with N turns along a length L (metres). N ÷ L is the turns per metre.
μ0 = 4π × 10−7 N A−2The permeability of free space, a constant on the data sheet. μ0 ÷ 2π = 2 × 10−7 exactly, a handy check.

Dot points: PY11-EM-40, PY11-EM-41, PY11-EM-42, PY11-EM-43, PY11-EM-44, PY11-EM-45, PY11-EM-46, PY11-EM-47 (2025 Physics syllabus, Year 11), in our own words.

Mini lesson

Field lines and the bar magnet

Field lines show two things. Their direction (the arrow) is the way the north pole of a small compass would point. Their spacing shows the strength: lines close together mean a strong field, lines spread out mean a weak one.

A bar magnet with north on the left and south on the right. Field lines leave the north pole, curve around above and below the magnet and enter the south pole. A dashed line inside the magnet continues from south back to north.NS
Outside: north to south. Inside (dashed): south to north, so every line is a closed loop. The lines are closest together at the poles.

Into and out of the page: dots and crosses

Many diagrams need a current or field that points straight into or out of the page. Imagine an arrow (or a dart). If it flies towards you, you see its point: a dot in a circle, ⊙, means out of the page. If it flies away from you, you see its tail feathers: a cross in a circle, ⊗, means into the page. The same symbols are used for currents, fields and forces.

A straight wire carrying a current has a field of circles centred on the wire. Find the direction with the right-hand grip rule: point your right thumb along the conventional current and your fingers curl the way the field goes. For current into the page (⊗), the field circles clockwise; for current out of the page (⊙), anticlockwise. The circles are drawn further apart as you go out, because the field gets weaker with distance.

Two straight wires seen end-on. Left: a cross in a circle (current into the page) surrounded by circular field lines going clockwise. Right: a dot in a circle (current out of the page) surrounded by circular field lines going anticlockwise.⊗ current into pagefield: clockwise⊙ current out of pagefield: anticlockwise
Right-hand grip rule: thumb along the current, fingers give the field. Into the page (⊗): clockwise. Out of the page (⊙): anticlockwise.

How strong is the field near a wire?

For a long straight wire, B = μ0I ÷ 2πr. The field is proportional to the current and inversely proportional to the distance: double the current and B doubles; go twice as far away and B halves (it is 1 ÷ r, not 1 ÷ r2).

Fields are vectors. If two wires both make a field at the same point, find each one's size and direction with the grip rule, then add them: same direction, add the sizes; opposite directions, subtract.

Loops and solenoids

Bend the wire into a loop and the circles from every part of the loop point the same way through the middle, so the field is concentrated inside the loop. Seen edge-on, the loop is a ⊙ at one side and a ⊗ at the other.

A current loop seen edge-on: the top of the loop carries current out of the page and the bottom carries current into the page. Small circles of field surround each side, and a field line runs straight through the middle of the loop from left to right, returning around the outside.outin
A single loop, edge-on. Inside the loop the fields from both sides point the same way (to the right here), so the field is strongest through the middle.

The solenoid

A solenoid is a long coil of insulated wire wound in a helix, usually around a tube, with many turns side by side. With a direct current through it, the loops' fields add: inside, the field is strong, uniform and parallel to the axis; outside, it looks like the field of a bar magnet, with a north pole at one end and a south pole at the other.

Find the poles with the right-hand grip rule for coils: curl your fingers the way the current goes around the turns, and your thumb points to the north end. The field strength inside is B = μ0NI ÷ L. It depends on the turns per metre (N ÷ L) and the current, not on the coil's diameter.

In the cross-section below, the current comes out of the page along the top of each turn (⊙) and goes into the page along the bottom (⊗). The grip rule puts the north pole on the right.

Cross-section of a solenoid: a row of dots along the top (current out of the page) and a row of crosses along the bottom (current into the page). Straight, evenly spaced field lines run left to right inside, leaving the north pole on the right and looping around the outside back to the south pole on the left.SN
Inside a solenoid the field is uniform (parallel, evenly spaced lines). Outside it matches a bar magnet: N on the right here, S on the left.

Electromagnets: what makes them stronger

An electromagnet is a solenoid wound on a core. From B = μ0NI ÷ L, you make it stronger with more current, or more turns on the same length. Stretching the same coil longer spreads the turns out and makes it weaker.

The biggest gain comes from the core. A ferromagnetic core (iron, or alloys such as silicon steel) becomes magnetised by the coil's field and adds its own, multiplying the field by hundreds or thousands of times, so B = μ0NI ÷ L only applies to an air (empty) core. Soft iron is chosen for electromagnets that must switch off, such as relays and scrapyard lifting magnets, because it magnetises easily and loses its magnetism as soon as the current stops. Hard steel keeps its magnetism, which suits permanent magnets but not a switchable electromagnet. Copper, aluminium and plastic are not ferromagnetic, so they add nothing.

In the practical, change one variable at a time (current, number of turns, core material) and measure the strength in the same way each time, for example the number of paper clips lifted or a magnetic field sensor reading at a fixed distance.

Common mistakes

Mini quiz

6 quick questions. Pick an answer to see if you're right and why.

  1. Which statement about magnetic field lines is correct?
    Show answer

    B. The field has only one direction at each point, so lines can't cross. They are closed loops (not ending at the poles), they crowd together where the field is strong, and they run N to S outside a magnet.

  2. A long straight wire carries a current into the page (⊗). Viewed on the page, the magnetic field lines around it are:
    Show answer

    A. Point your right thumb into the page: your fingers curl clockwise as you look at the page. Out of the page (⊙) would be anticlockwise.

  3. The distance from a long straight current-carrying wire is tripled. The magnetic field strength becomes:
    Show answer

    B. B = μ0I ÷ 2πr, so B ∝ 1 ÷ r. Three times the distance gives one-third of the field. One-ninth would be an inverse-square law, which this is not.

  4. A solenoid 20 cm long has 800 turns and carries 1.5 A. What is the magnetic field strength inside it?
    Show answer

    A. B = μ0NI ÷ L = 4π × 10−7 × 800 × 1.5 ÷ 0.20 = 7.5 × 10−3 T. Leaving L as 20 (cm) gives 7.5 × 10−5 T; leaving out N gives 9.4 × 10−6 T; multiplying by L gives 3.0 × 10−4 T.

  5. Which core material is best for an electromagnet in a scrapyard crane that must drop its load when the current is switched off?
    Show answer

    B. Soft iron is ferromagnetic, so it strengthens the field a lot, and it loses its magnetism when the current stops. Hard steel stays magnetised (the load wouldn't drop), and copper and aluminium are not ferromagnetic.

  6. Which change would make the field inside an air-cored solenoid weaker?
    Show answer

    C. B = μ0NI ÷ L: the same N over twice the L halves the turns per metre, so B halves. Reversing the current swaps the poles but keeps the same strength.

Worked example

Two long straight wires, X and Y, are perpendicular to the page and 10.0 cm apart. Wire X carries 6.0 A out of the page and wire Y carries 4.0 A into the page. Point P lies on the line between them, 3.0 cm from X.

Calculate the magnitude and direction of the net magnetic field at P.

(5 marks)

I'll think out loud, the way you should in the exam, using KNOW-UD: Knowns, Not known, Organise, Work it out, Units, Direction.

Prediction first. The currents are in opposite directions and P is between the wires, so I expect the two fields at P to point the same way and add. X has the bigger current and is much closer, so its field should dominate: roughly 4 × 10−5 T from X plus about a quarter of that from Y. I predict about 5 × 10−5 T.

K · Knowns

I draw the wires end-on with the right symbols: X out of the page is a dot, Y into the page is a cross. P is 3.0 cm from X, so it is 10.0 − 3.0 = 7.0 cm from Y. I convert to metres straight away.

  • IX = 6.0 A (out of the page), rX = 3.0 cm = 0.030 m
  • IY = 4.0 A (into the page), rY = 7.0 cm = 0.070 m
  • μ0 = 4π × 10−7 N A−2
Two wires seen end-on, 10 cm apart: X on the left carries 6.0 A out of the page (dot symbol) and Y on the right carries 4.0 A into the page (cross symbol). Point P lies between them, 3.0 cm from X and 7.0 cm from Y, where the net field is unknown.PB = ?X: 6.0 Aout of pageY: 4.0 Ainto page3.0 cm7.0 cm
Knowns on the sketch: X carries 6.0 A out of the page, Y carries 4.0 A into the page, P is 3.0 cm from X and 7.0 cm from Y. Unknown: the net field B at P.

N · Not known

The question wants a field, which is a vector, so my answer needs a size in tesla and a direction.

  • Bnet at P = ? T, and its direction

O · Organise

Each wire makes its own field at P, so I use B = μ0I ÷ 2πr twice. I find each direction with the grip rule before adding, because the directions decide whether I add or subtract.

  • BX = μ0IX ÷ 2πrX, BY = μ0IY ÷ 2πrY
  • X (⊙, anticlockwise field): P is to the right of X, so BX points towards the top of the page
  • Y (⊗, clockwise field): P is to the left of Y, so BY also points towards the top of the page
  • Same direction, so Bnet = BX + BY

W · Work it out

μ0 ÷ 2π is 2 × 10−7, which keeps the calculator work short. I keep full values until the end.

  • BX = (4π × 10−7 × 6.0) ÷ (2π × 0.030) = 4.0 × 10−5 T
  • BY = (4π × 10−7 × 4.0) ÷ (2π × 0.070) = 1.1429 × 10−5 T
  • Bnet = 4.0 × 10−5 + 1.1429 × 10−5 = 5.1429 × 10−5 T

U · Units

μ0 in N A−2 times amperes over metres gives N A−1 m−1, which is the tesla. The data are to two significant figures, so I give two.

  • Bnet ≈ 5.1 × 10−5 T

D · Direction

Both fields point towards the top of the page at P, so the net field does too. I say it relative to the page, not just 'up', so nobody can read it as out of the page.

  • Bnet = 5.1 × 10−5 T, in the plane of the page, towards the top of the page (at right angles to the line XY)

The net magnetic field at P is 5.1 × 10−5 T, towards the top of the page (in the plane of the page, perpendicular to the line joining the wires).

Check against the prediction. I predicted about 5 × 10−5 T with the two fields adding. I got 5.1 × 10−5 T, with X giving most of it (4.0 × 10−5 T), as expected for the closer wire with the bigger current.

Exam advice

What markers look for

Summaries in our own words. Read NESA's own feedback with the exam packs: 2019 · 2021 · 2024.

Where this leads in Year 12

Year 12 Electromagnetism starts from these fields. A magnetic field pushes on a moving charge (F = qvB sin θ) and on a current-carrying wire (F = lIB sin θ), which gives circular paths for charged particles and the torque that turns electric motors. Then magnetic flux (Φ = BA cos θ) and its changes lead to electromagnetic induction, Lenz's law (where the grip rule from this topic gives the induced current's direction), generators and transformers.

FAQ

What do the dot and cross mean in magnetic field diagrams?
A dot in a circle (⊙) means out of the page, towards you, like the point of an arrow coming at you. A cross in a circle (⊗) means into the page, away from you, like an arrow's tail feathers. They are used for currents, fields and forces.
Are B = μ0I/2πr and B = μ0NI/L on the data sheet?
Yes. NESA's sample data sheet for the new (2025) syllabus includes both, along with the value of μ0 = 4π × 10−7 N A−2. Check which sheet your school gives you for Year 11 exams.
How does the right-hand grip rule work for a solenoid?
Curl the fingers of your right hand around the solenoid in the direction the conventional current flows through the turns. Your thumb then points along the axis to the north end of the solenoid.
What is the difference between the field of a wire and the field of a solenoid?
Around a straight wire the field lines are circles centred on the wire, and the field weakens with distance (B ∝ 1 ÷ r). Inside a solenoid the field is straight, uniform and along the axis, and outside it looks like a bar magnet's field.
Why is soft iron used for electromagnet cores?
It is ferromagnetic, so it multiplies the coil's field many times, and it is magnetically soft: it magnetises easily and loses its magnetism as soon as the current is switched off, so the electromagnet can be turned off.

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