Understand magnetic fields and forces the easy way, with plain English intuition, an interactive simulation, the right hand rule, the forces on wires and moving charges, worked examples and an auto marked practice test. VCE Physics Units 3 and 4.
Learn
Hold a magnet near a compass and the needle swings. That invisible push reaching out from the magnet is a magnetic field, and the surprising part is that a wire carrying a current makes one too. Drop a current carrying wire into a magnetic field and the wire suddenly feels a force, a real shove you can measure. Master where that force comes from and which way it points, and you have the heart of every electric motor.
Fields you cannot see
A magnetic field is the region around a magnet or a current where magnetism can be felt. We give it the symbol B and measure it in tesla (T).
Because the field points into and out of the page in so many problems, physicists use a neat shorthand for drawing it:
A field pointing into the page is drawn as a grid of crosses, like the tails of arrows flying away from you.
A field pointing out of the page is drawn as a grid of dots, like the tips of arrows flying towards you.
A current also makes its own field, which is exactly why a wire and a magnet can push on each other.
The grey line is the wire, the blue arrow is the currentI flowing along it, and the crosses are the fieldB pointing into the page. The red arrow is the forceF the wire feels, and notice it points straight up, at right angles to both the current and the field.
The force on a wire
Put a current carrying wire across a magnetic field and it feels a force. The size of that force depends on four things, all multiplied together: how many loops of wire there are, how strong the field is, how big the current is, and how long the wire is.
F=nBIL
Here n is the number of loops, B is the field in tesla, I is the current in amperes and L is the length of wire in the field. The force is greatest when the wire is perpendicular to the field, and it shrinks to zero when the wire lies along the field.
The force on a moving charge
A current is really just charges on the move, so a single moving charge feels a force in a magnetic field too. For one charge q moving at speed v across a field B, the force is their product.
F=qvB
This force is always perpendicular to the velocity, which means it never speeds the charge up or slows it down. Instead it bends the path, curving a fast charge into a circle.
See it for yourself
Move the bar magnet around, flip its poles, and watch the field lines redraw. Then switch to the electromagnet and see how a current in a coil of wire builds a magnetic field of its very own, just like the bar magnet.
Decide whether you have a wire or a single moving charge. Use F=nBIL for a wire and F=qvB for a charge.
Check the geometry. These formulas give the full force only when the current or velocity is perpendicular to the field.
Substitute the numbers, keeping the powers of ten lined up when you work in scientific notation.
For direction, use the right hand rule, remembering the force always comes out at right angles to both the motion and the field.
Lock it in with active recall
Cover the answer and say each one out loud before you flip. Rate yourself honestly — the cards you find hard come back sooner, the ones you know are spaced further out.
Active recall
Answer from memory first, then flip. Rate yourself and each card returns on a spaced schedule (1 → 3 → 7 → 16 days).
Write the force formula for a current carrying wire and name each symbol.
F=nBIL — n loops, field B in tesla, current I in amperes, L the length of wire in the field.
Write the force formula for a single moving charge in a magnetic field.
F=qvB — charge q, speed v, field B (when v is perpendicular to B).
When is the force on a wire greatest, and when is it zero?
Greatest when the wire is perpendicular to the field; zero when the wire lies parallel to the field.
How do you find the direction of the magnetic force?
The right hand rule: thumb along the current I, fingers along the field B, palm pushes in the direction of the force F. Reverse for a negative charge.
How is a field pointing into the page drawn versus out of the page?
Into the page: a grid of crosses (arrow tails). Out of the page: a grid of dots (arrow tips).
Why does the magnetic force on a moving charge never change its speed?
The force is always perpendicular to the velocity, so it does no work. It bends the path into a circle but leaves the speed unchanged.
Recall · Charged Particles in Fields
A charge enters a magnetic field at right angles. What radius circle does it trace?
r=qBmv — the magnetic force qvB supplies the centripetal force rmv2.
Recall · DC Motors
Why do the two sides of a motor coil feel forces in opposite directions?
The current runs the opposite way along each side, so F=nBIL pushes one side up and the other down, twisting the coil (torque).
See the recipe in action in the Worked Examples tab, then test yourself in Try It.
Worked examples
Worked Example 1Force on a current carrying wire
A straight wire of length 0.50 m carries a current of 3.0 A at right angles to a 0.40 T magnetic field. Taking a single wire (n=1), find the force on it.
1
The wire is perpendicular to the field, so it feels the largest possible force. Use the wire force rule with n=1.
F=nBIL=BIL
2
Substitute the field, current and length.
F=0.40×3.0×0.50
3
Multiply through to get the force in newtons.
F=0.60 N
Answer
F=BIL=0.40×3.0×0.50=0.60 N
Worked Example 2Force on a moving charge
A charge of 1.6×10−19 C moves at 2.0×106 m/s at right angles to a 0.50 T magnetic field. Find the magnetic force on it.
1
The charge moves perpendicular to the field, so use the moving charge rule directly.
F=qvB
2
Substitute the charge, speed and field.
F=1.6×10−19×2.0×106×0.50
3
Multiply through to get the force in newtons.
F=1.6×10−13 N
Answer
F=qvB=1.6×10−19×2.0×106×0.50=1.6×10−13 N
Practice questions
Practice test
Try it yourself
6 questions, 9 marks
Choose your answers, then submit to see your score and the full worked solutions.
Multiple choice is marked for you, just like Exam 2 Section A.
Q1.A straight wire of length 0.20 m carries a current of 5.0 A perpendicular to a 0.30 T magnetic field. The force on the wire is closest to:
1mark
Need a hint?
Use F=BIL with a single wire.
Show worked solution
With a single wire, F=BIL=0.30×5.0×0.20=0.30 N. The wire is perpendicular to the field, so this is the full force with no angle factor to worry about.
Q2.A charge of 2.0×10−19 C moves at 3.0×106 m/s perpendicular to a 0.20 T magnetic field. The magnetic force on it is closest to:
1mark
Need a hint?
Use F=qvB and add the powers of ten carefully.
Show worked solution
F=qvB=2.0×10−19×3.0×106×0.20=1.2×10−13 N. The numbers give 2.0×3.0×0.20=1.2, and the powers give 10−19×106=10−13.
Q3.When is the force on a current carrying wire in a magnetic field at its greatest?
1mark
Need a hint?
Think about the orientation that lets the field act fully across the current.
Show worked solution
The force is largest when the wire is perpendicular to the field. When the wire lies parallel to the field there is no force at all, and any angle in between gives something smaller than the perpendicular maximum.
Q4.A coil of 10 loops, each of length 0.10 m, carries a current of 2.0 A perpendicular to a 0.50 T magnetic field. The force on the coil is closest to:
1mark
Need a hint?
Use F=nBIL and do not forget the number of loops n.
Show worked solution
F=nBIL=10×0.50×2.0×0.10=1.0 N. The number of loops multiplies the single wire force, so ten loops give ten times the force of one.
Q5.A straight wire of length 0.25 m carries a current of 4.0 A perpendicular to a magnetic field. The force on the wire is measured to be 0.50 N. Taking a single wire, find the magnetic field strength. Show your working.
3marks
Work this on paper. The worked solution appears once you submit.
Show worked solution
Start from the wire force rule with a single wire,
F=BIL.
Rearrange to make the field the subject,
B=ILF=4.0×0.250.50=1.00.50=0.50 T.
Q6.An electron travelling at 7.80×107 m/s enters a uniform magnetic field of 2.50×10−4 T at right angles, so it moves in a circular arc. Calculate the radius of its path to three significant figures (electron mass 9.11×10−31 kg, charge 1.6×10−19 C).
2marks
Work this on paper. The worked solution appears once you submit.
Show worked solution
The magnetic force provides the centripetal force, qvB=rmv2, so r=qBmv=1.6×10−19×2.50×10−49.11×10−31×7.80×107=1.78 m.
VCAA 2025 Physics Exam, Section B Q7
Frequently asked questions
What is a tesla?
The tesla, symbol T, is the unit of magnetic field strength. A field of one tesla is quite strong, so everyday magnets are usually measured in much smaller fractions of a tesla.
Why is the force zero when the wire lies along the field?
The magnetic force needs the current to cut across the field lines. When the wire points the same way as the field there is nothing for the field to push against, so the force drops to zero.
How do I find which way the force points?
Use the right hand rule. Line your fingers up with the current and the field as your course sets out, and your hand tells you the direction of the force, which always comes out at right angles to both.
