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IB Physics Magnetic Fields: Rules, Equations and Exam Tips

IB Physics Magnetic Fields: Rules, Equations and Exam Tips

11 min readOliver Kidd (Co-founder)31 Oct 2026

A magnetic field is a region where a moving charge or a current-carrying wire feels a force. In IB Physics you are asked to draw the field, find its direction with a hand rule, and calculate the force using F = qvB sin θ or F = BIL sin θ. This guide takes you through each step, with worked examples and the mistakes examiners see most often. It also covers Kirchhoff’s laws, because students usually revise them in the same block as electromagnetism.

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TL;DR

  • Field lines show direction by their tangent and strength by how close together they are. They always form closed loops.
  • Use the right-hand grip rule for the field around a wire, and the right-hand force rule for the force on a moving charge or current.
  • The magnetic force is always perpendicular to the velocity, so it changes direction but never speed. That is why charges move in circles.
  • Kirchhoff’s junction rule conserves charge and the loop rule conserves energy. Sign care is where the marks are won.
  • Practise with exam-style questions and mark schemes, not just notes.

Table of Contents

What a magnetic field is and how to draw it

A magnetic field is defined by what it does: it exerts a force on a charged particle moving through it. Magnets and moving charges (currents) create it. Its unit is the tesla (T).

In a diagram, field lines are a vector-field picture. The direction of the field at any point is the tangent to the line there, and closer lines mean a stronger field. The same page explains that magnetic field lines form continuous closed loops. Outside a bar magnet they run from north to south, and inside the magnet they return from south to north.

Three diagrams come up again and again:

  1. Bar magnet. Lines leave the north pole, curve round and enter the south pole. They are densest near the poles.
  2. Long straight wire. The lines are concentric circles centred on the wire, drawn further apart as the distance grows because the field weakens.
  3. Solenoid. A near-uniform field inside, parallel evenly spaced lines, and a bar-magnet-like pattern outside.

When the field is perpendicular to the page, use the standard symbols. A dot means the field points out of the page towards you, and a cross means it points into the page. Think of the tip and the tail of an arrow.

A tip for diagrams: always add arrowheads, and draw lines that never cross. Examiners deduct for lines that cross or have no direction.

The hand rules: finding direction without guessing

Students search for the “three-finger rule”, but names differ between textbooks and teachers. Learn the two jobs, then use whichever hand rule you were taught, consistently.

Job 1: the field around a current

The right-hand grip rule gives the field direction. Point your right thumb along the conventional current, and your curled fingers show the direction of B circling the wire. For a solenoid, curl your fingers in the direction of the current in the coils. Your thumb then points to the north end.

Job 2: the force on a moving charge or current

Here you need three directions: velocity (or current), field and force. A common version is: first finger along the field, second finger along the velocity or conventional current, thumb gives the force. Other versions use a flat palm. All of them agree if you use them carefully.

For a positive charge, the force is perpendicular to both velocity and field, and it follows the right-hand rule. For a negative charge, the force is in the opposite direction. In a current, always use conventional current. Electrons move the other way.

The equations and when to use them

The force on a charge q moving at speed v through a field B, with θ the angle between v and B, is:

F = qvB sin θ

For a straight wire of length L carrying current I in a field B, the force is:

F = BIL sin θ

Both are in the data booklet, so you do not need to memorise them. Check the current version for your exam session, though. You do need to know what each symbol means and when sin θ equals 1 (field at right angles) or 0 (field parallel, no force).

Because the force is always perpendicular to the velocity, it does no work on the charge. Speed stays constant and only direction changes. That is the key idea behind circular motion. Set the magnetic force equal to the centripetal force:

qvB = mv²/r, so r = mv/(qB)

A faster particle moves in a bigger circle. A heavier particle also moves in a bigger circle. A stronger field gives a tighter circle.

The equations and when to use them

Worked examples

Example 1: force on a wire

A 0.20 m length of wire carries 5.0 A at right angles to a uniform 0.30 T field. Find the force.

F = BIL sin θ = 0.30 × 5.0 × 0.20 × sin 90° = 0.30 N

If the wire is turned so that it makes 30° with the field, the force falls to 0.30 × sin 30° = 0.15 N. Show the substitution in every step, as marks go for method.

Example 2: a proton in a circle

A proton (mass 1.67 × 10⁻²⁷ kg, charge 1.60 × 10⁻¹⁹ C) enters a 0.50 T field at right angles with a speed of 2.0 × 10⁶ m s⁻¹. Find the radius.

r = mv/(qB) = (1.67 × 10⁻²⁷ × 2.0 × 10⁶) / (1.60 × 10⁻¹⁹ × 0.50) ≈ 4.2 × 10⁻² m

That is about 4.2 cm. Then sketch the path: a circle, with the force pointing towards the centre at every point. If the question asks for an electron, the circle curves the other way.

Common mistakes to avoid

These are patterns teachers see in student scripts, so check yourself against them:

  • Using electron flow instead of conventional current in a hand rule. This reverses the answer.
  • Forgetting that a negative charge flips the force direction.
  • Saying the magnetic force speeds the particle up. It cannot, because it is perpendicular to the motion.
  • Missing the angle. If the velocity is not at 90° to the field, use sin θ, or resolve the velocity into components.
  • Drawing field lines that stop. They form closed loops.
  • Mixing up dot and cross when the question gives a field into or out of the page.
  • Leaving out units. Give the tesla, newton or metre as required, and keep standard form tidy.

Where Kirchhoff’s laws fit

Kirchhoff’s laws sit in the electric circuits part of the course, not in magnetism. Even so, many students revise them in the same sitting, so here is the short version.

Junction rule: the current entering a junction equals the current leaving it. This conserves charge. Loop rule: the algebraic sum of potential changes around any closed loop is zero. This conserves energy. These two rules apply conservation of charge and energy, and they matter most for circuits that series and parallel rules cannot simplify.

A reliable method:

  1. Label the current in each branch and assume a direction. If you guess wrong, the answer simply comes out negative.
  2. Write the junction equation.
  3. Choose a loop direction and write the loop equation. Crossing a resistor in the direction of current is a potential drop, and crossing a cell from negative to positive terminal is a gain.
  4. Solve the simultaneous equations, then check by substituting into a different loop.

The usual error is a sign slip in step 3. Mark the direction of travel on your diagram before you write anything.

How we approach this topic at Tiber Tutor

We have found that magnetic fields reward practice more than rereading. Students who understand the three directions, and who practise sketching them, tend to answer the hardest questions calmly. Students who only memorise a hand rule can lose marks when the question gives a negative charge or an unusual diagram.

How we approach this topic at Tiber Tutor

That is why our IB Physics material is written by IB examiners and organised so that notes, animated videos, flashcards, exam-style questions and mark schemes link to each other. After a notes page, you move straight into questions on that same sub-topic. Our progress tracking and performance analytics then show which topics need more work, so your revision time goes where it counts. To our knowledge, no other IB STEM platform joins these pieces so tightly. Because the content comes from actual IB examiners and is kept aligned with the current syllabus, we believe it gives the best value for money in IB revision.

My advice: do one magnetism question a day for a fortnight, and mark it against the scheme honestly. Confidence follows quickly.

— Oliver

Practise with exam-style questions

If you want to check your understanding, our IB students page shows how the platform works. Every plan starts with a free 7-day trial. After that, the Per-Subject Plan is $9 per month and the All-Access Plan is $19 per month, both on our pricing page.

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You can use the test builder to put together a set of questions on one topic, review your own answers against examiner mark schemes, and watch your weak spots shrink over time.

FAQ

What is the hardest unit in IB Physics?

It depends on the student. Many find fields, quantum topics and the more abstract parts of the course demanding, because they mix maths with spatial thinking. Magnetic fields become much easier once you practise the hand rules and the circular-motion link.

What is the three-finger rule in physics?

It is a hand rule for finding the direction of the magnetic force. Your fingers represent field, current or velocity, and force, in the order your teacher uses. For a negative charge, reverse the result, and always use conventional current.

Do I need to memorise the magnetic force equations?

No. F = qvB sin θ and F = BIL sin θ are given in the IB data booklet. You must know how to apply them, including the angle and the direction of the force.

Are Kirchhoff’s laws part of magnetic fields?

No. They belong to electric circuits. The junction rule conserves charge and the loop rule conserves energy, and you use both to analyse circuits with more than one loop.

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