IB Physics HLTopic 4 — Force FieldsPaper 1 & 2Right-hand grip rule~17 min read
Magnetic Fields
Everything so far has been about charges sitting still. Now let them move, and a completely new field appears — one that no stationary charge can produce, no matter how big. A current in a wire makes it. A permanent magnet makes it, because deep inside, electrons are circulating. And unlike the electric field, this one does not point away from anything. It curls.
📘 What you need to know
A magnetic field is a region of space in which a magnetic pole experiences a force
It is created by moving charge or by permanent magnets. A stationary charge makes no magnetic field
Also called a B-field. Field lines run from the north pole to the south pole
Magnetic flux density B: the number of field lines passing through a region of space per unit area
Measured in teslas (T). One tesla is the flux density causing a force of 1 N on a 1 m wire carrying 1 A at right angles to the field
Field lines closer together → higher flux density → stronger field. They never cross
Around a straight wire: concentric circles, closest to the wire. Use the right-hand grip rule
Around a solenoid or flat coil: the field looks like a bar magnet. Fingers curl with the current, thumb points to north
Viewed end-on, the end where the current runs anticlockwise is the north pole
Current means conventional current (+ to −), never electron flow
What makes a magnetic field
Two sources, and they are secretly the same one.
Moving electric charge. A current in a wire is electrons on the move, and a magnetic field wraps around it
Permanent magnets. Materials that produce a field of their own
A charge sitting still produces an electric field and nothing else. Set it moving and a magnetic field appears around it. Motion is the whole ingredient.
Then why does a bar magnet, lying motionless on the bench, have a field? Because inside it nothing is motionless. Electrons in the iron are spinning and orbiting, and in a magnetised material those tiny circulating currents all line up instead of cancelling. A permanent magnet is not a different kind of source. It is billions of moving charges, agreeing.
You cannot see a magnetic field, but you can watch it work: iron filings snap into line along it, and a plotting compass swings to follow it.
Flux density, and the tesla
Magnetic flux density — definitionthe number of magnetic field lines passing through a region of space per unit area
One teslathe flux density causing a force of 1 N on a 1 m wire carrying 1 A at right angles to the fieldso B = F / IL • 1 T = 1 N A−1 m−1
A tesla is enormous. The Earth’s field is about 50 microteslas; a fridge magnet manages a few millitesla; an MRI scanner runs at 1.5 to 3 T and needs superconducting coils to do it. If your answer to a flux density question comes out in whole teslas, look again at the question — or be very impressed with the apparatus.
Bar magnets
Field lines emerge from the north pole and re-enter at the south. The arrow at any point shows the direction of the force a free magnetic north pole would feel there.
These lines were computed from the field of the two poles, not sketched. They leave the north pole, curve round, and land on the south — and they bunch together at the ends, which is exactly why the poles are the strong bits.
Two magnets together
Between the attracting pair, the lines cross the gap almost straight and parallel — a nearly uniform field. Between the repelling pair, they refuse to meet, and a neutral point opens up in the middle.
You have seen that neutral point twice already this topic. Two like electric charges have one. Two like magnetic poles have one. In both cases two vectors of equal size point opposite ways and cancel. Physics reuses its ideas shamelessly, and that is very good news for you.
Uniform magnetic fields
Hold two opposite poles close together and the field between them is uniform: the same strength and direction everywhere, drawn as equally spaced parallel lines running from N to S. Same picture as the field between charged parallel plates.
The Earth’s field
A compass needle, left alone, swings until its north pole points north. Since unlike poles attract, the thing it is pointing at must be a magnetic south pole. So the Earth’s magnetic south pole sits near the geographic north pole. The Earth behaves like a bar magnet buried the wrong way round.
The field around a current-carrying wire
Send a current down a straight wire and the field lines form concentric circles centred on the wire. They are packed tightly near the wire, where the field is strongest, and spread out with distance.
The circles are drawn at equal steps of B. Since B falls off with distance, they get further apart — radii of 14, 19, 28 and 56 units, gaps of 5, 9 and 28.
The right-hand grip rulepoint your right thumb along the conventional current and your curled fingers point along the magnetic field
Conventional current, remember: from + to −, the direction a positive charge would drift. The electrons are actually going the other way. Use the electron direction and you will get a field that points exactly backwards, and lose the mark for a rule you actually knew.
Solenoids and coils
Bend the wire into a loop and the circles around each bit of wire reinforce one another through the middle. Stack many loops into a coil — a solenoid — and you have crammed a great many field lines into a small space. High flux density. A strong field. An electromagnet.
A flat circular coil is simply one turn of this. The lines emerge from one face (north) and enter the other (south), and the same grip rule finds which is which.
Moving charge
makes a
Magnetic field
whose direction comes from
the right-hand grip rule
Source
Shape of the field
Finding the direction
Bar magnet
Loops from N round to S
Arrows out of N, into S
Straight wire
Concentric circles round the wire
Thumb along I, fingers curl with B
Solenoid or flat coil
Exactly like a bar magnet
Fingers curl with I, thumb points to N
Two opposite poles, close
Uniform — parallel, equally spaced
Straight across, N to S
🧭 Working a magnetic field question
Is anything moving? No current, no motion, no magnet → no magnetic field.
Use conventional current (+ to −). Not electron flow. Ever.
Straight wire? Right-hand grip: thumb along I, curled fingers give B.
Solenoid or coil? Fingers curl the way the current goes; the thumb points to the north pole.
End-on view? Current anticlockwise → you are looking at the north pole.
Sketching? Arrows on every line, N to S, never crossing, equally spaced if uniform.
WE 1
A straight wire of length 25 cm carries a current of 3.0 A at right angles to a uniform magnetic field. The force on the wire is 0.15 N. (a) Calculate the magnetic flux density. (b) Comment on the size of your answer.
(a) Step 1 — use the definition of the tesla directlyone tesla gives 1 N on a 1 m wire carrying 1 A, so B = F / ILStep 2 — convert and substituteL = 25 cm = 0.25 mB = 0.15 / (3.0 × 0.25) = 0.15 / 0.75B = 0.20 T(b) Step 3 — is that plausible?
The Earth’s field is about 50 μT; a fridge magnet a few mT.
0.20 T is a strong laboratory magnet — large, but reasonableThe “at right angles” matters. Tilt the wire and the force falls; lay it along the field and the force vanishes altogether. The tesla is defined at 90° for exactly that reason.
WE 2
A long vertical wire carries a conventional current downwards. (a) Describe the shape of the magnetic field in a horizontal plane through the wire. (b) State the direction of the field at a point due north of the wire. (c) State what happens if the current is reversed.
(a) the shapeconcentric circles centred on the wire, in the horizontal plane.
Closest together near the wire, spreading out with distance.
circular field lines, strongest at the wire(b) apply the right-hand grip rule
Right thumb points downwards, along the current.
The curled fingers then run clockwise when viewed from above.
Going clockwise from due north takes you towards the east.
the field points due east(c) reverse the currentthe field reverses: it now points due west at that pointDraw it. Put your right thumb down the page, look at the back of your hand, and read the fingers off. The commonest error here is using electron flow — which would hand you west when the answer is east.
WE 3
Viewed from its left-hand end, the current in a solenoid appears to flow clockwise. (a) Identify the north pole. (b) State the direction of the magnetic field inside the coil. (c) Suggest two ways to increase the flux density of the solenoid.
(a) which end is north?
An end where the current runs anticlockwise is a north pole.
Seen from the left the current is clockwise, so that end is south.
the right-hand end is the north pole(b) the field inside
Inside a solenoid the field runs from the south end to the north end.
from left to right, along the axis(c) making it strongermore turns of wire in the same lengtha larger currentA third way, worth knowing: slide an iron core inside. Flux density is field lines per unit area, so anything that packs more lines into the same space raises B — more turns, more current, or a material that concentrates the field.
💡 Top tips
A stationary charge makes no magnetic field. Motion is the whole ingredient.
Field lines run N to S outside a magnet, and S to N inside it (and inside a solenoid).
Always use conventional current, + to −, in the grip rule.
Solenoid: fingers curl with the current, thumb points to north. End-on, anticlockwise = north.
Arrows on every line. Lines never cross. Equally spaced only if the field is uniform.
Quote the tesla properly: 1 N on a 1 m wire carrying 1 A at right angles.
Sanity-check flux densities: Earth ≈ 50 µT, fridge magnet ≈ mT, MRI ≈ a few T.
⚠ Common mistakes
Using the left hand, or using the electron flow direction, in the grip rule
Saying a stationary charge produces a magnetic field. It produces an electric one only
Drawing field lines from S to N outside the magnet, or leaving the arrows off entirely
Letting magnetic field lines cross. They never do
Drawing circles around a wire equally spaced. They spread out, because B weakens with distance
Forgetting the Earth’s magnetic south pole is at the geographic north
Thinking the field between two repelling poles is simply “zero everywhere”. It is zero at one point
Omitting “at right angles” from the definition of the tesla
Quick recap: A magnetic field is a region where a magnetic pole feels a force. It is made by moving charge or by permanent magnets — never by a charge at rest. Flux density B is the field lines per unit area, measured in teslas: 1 T gives 1 N on a 1 m wire carrying 1 A at right angles. Lines run N to S, never cross, and crowd together where the field is strong. Around a straight wire they are concentric circles that spread out with distance; around a solenoid they copy a bar magnet. The right-hand grip rule gives every direction: thumb along the conventional current, fingers curl with B — and for a coil, the thumb points to north.
Notice what we have not done. We have described this field in loving detail — its shape, its direction, its strength — and never once asked what it does. Yet the tesla was defined by a force on a wire, which rather gives the game away. Put a current in a magnetic field and it is pushed sideways, in a direction perpendicular to both. Fire a single charge across the field and it is pushed sideways too — and being pushed sideways forever means going in a circle. Next: the magnetic force, on a current and on a moving charge.
Right-hand grip rule not sticking?
Book a free meeting and we’ll drill wires, solenoids and the anticlockwise-equals-north trick until your hand does it without you.
