Diagnostic · Magnetic force & motion
Motion in Electromagnetic Fields Diagnostic
Maps what your students think a magnetic field does to a charge and to a current, from a charge at rest to two parallel wires. It shows which band to address first.
IB DP · AP · A-Level · GCSE / IGCSE
1
Forms
22
Questions
~30
Minutes
11
Bands
FundaFirst HS diagnostics have run in classrooms at 10 schools · 9 countries · 3 continents
The wrong ideas come from physics education research, which has recorded them since the 1970s: Viennot, Trowbridge & McDermott, Arons, Hestenes, Maloney. The physics comes from Arons, Knight, Moore, and Chabay & Sherwood.
What it maps
Eleven misconception bands across five families, two questions each.
RST-1
A stationary charge feels no magnetic force from B alone
The place to start. F = q(v × B) contains the velocity, so an ion held at rest in a uniform field feels no magnetic force, however strong the field. Moving at right angles to the same field, it feels |q|vB. Read this band first. Its result does not decide whether any other band is flagged.
EQV-1
Electric and magnetic interactions are not interchangeable
Magnetic poles carry no electric charge. Leaving electric polarisation aside, a charged rod that is not magnetic does not turn a neutral magnet. In a uniform magnetic field, a magnet at an angle to the field is turned towards it. In a uniform electric field it is not turned at all.
DIR-1
Moving-charge force depends on direction, sign and angle
The force is perpendicular to both v and B, with its direction from q(v × B). A positive charge moving right through a field into the page is pushed up the page. Its size is |q|vB sin θ, where θ is the angle between v and B. It is zero at 0°, half of |q|vB at 30° and |q|vB at 90°.
MWS-1
Magnetic force changes direction, not speed
The magnetic force on a moving charge does no work. With no other force acting, the speed after a quarter-turn is unchanged. In a uniform field the velocity component along B is unchanged too. A particle that enters at an angle to B follows a helix at constant speed.
ORB-1
Orbit timing follows q, m and B, not speed or radius
Below relativistic speeds the period is T = 2πm/(|q|B). Doubling the speed doubles the radius and leaves the period unchanged. The radius relation r = mv/(|q|B) also gives the charge-to-mass ratio from a measured path, as |q|/m = v/(Br).
ORB-2
The bend of the path and the sign of the charge set which way it goes round
The sign of q enters the force. An electron moving right through a field into the page curves down the page, clockwise as seen. A track that bends to the side opposite to v × B shows that an unknown charge is negative.
SEL-1
Crossed fields select one speed by force balance
In a velocity selector the particle moves at right angles to both fields, and the electric and magnetic forces are opposed. They balance at one speed, v = E/B, so a straight path needs E = vB. A slower particle feels the smaller magnetic force and is deflected towards the electric force.
LAW-1
The wire-force law comes from forces on moving carriers
For a wire at right angles to B, F = BIL is the sum of the q(v × B) forces on the moving carriers in length L. Electron carriers drift against the conventional current, so both v and q are reversed. The force on the wire is unchanged.
SEG-1
The force on a loop depends on which parts are in the field
A rectangular loop lies at right angles to a uniform field, with its lower side in the field and its upper side outside. The forces on the parts of the two vertical sides inside the field cancel. The net force comes from the lower side alone. For 0.20 T, 3.0 A and a 0.40 m lower side, it is 0.24 N.
COL-1
Many slow carriers can produce a measurable wire force
The magnetic force acts on the drifting electrons, and the field exerts no net force on the stationary lattice. In a steady current, the electric field of charge built up on the sides of the wire passes the force to the lattice. Many carriers, each with a small force, give 1.0 N for 2.0 A in 0.50 T over 1.0 m.
PWI-1
Neutral parallel wires carrying currents interact magnetically
Each current’s magnetic field exerts a force on the other current. Currents in the same direction attract, and currents in opposite directions repel. Reversing one current reverses the force. The questions test the mechanism, and each one states whether the wires attract or repel.
The five families are the force on one charge, motion in a magnetic field, crossed fields, the force on a wire, and the force between wires. The diagnostic does not test motion in a uniform electric field. It does not ask students to find the direction of the field around a straight wire, and gives that direction where a question needs it.
A question from it
Students can put numbers into F = qvB and F = BIL and still hold these ideas.
The field pushes a resting charge
An ion is held at rest in a uniform magnetic field. The tempting answer gives it a force, along the field or across it. The magnetic force is F = q(v × B), so with v = 0 it is zero, however strong the field. Moving at right angles to B, the ion feels |q|vB. The orbit, selector and wire bands all build on this.
The field changes the speed
A positive particle bends round a circular arc in a uniform magnetic field. Because the force keeps acting, the tempting answer has the field speeding the particle up or slowing it down. The magnetic force is perpendicular to the velocity at every instant, so it does no work. With no other force acting, the speed stays the same. Hearing “accelerates” as “speeds up” makes this error easy to keep.
Any speed goes straight through
In a velocity selector the electric and magnetic forces point opposite ways. The tempting account says the fields balance, so E equals B and any particle goes straight through. It is the forces that balance. The electric force |q|E is the same at every speed, while the magnetic force |q|vB grows with speed. They cancel only at v = E/B. A slower particle bends towards the electric force.
Slow drift, no force
The electrons in a wire drift very slowly. The tempting conclusion is that their magnetic force is too small to matter, so the field must pull on the metal itself. Each carrier’s force is small, but the wire holds an enormous number of carriers. Together they give F = BIL, which is 1.0 N for 2.0 A in 0.50 T over 1.0 m. Charge building up on one side passes the push to the metal.
The wires pull electrically
Two long, parallel, neutral wires carry currents in the same direction and attract. The tempting explanation is electric, with the wires oppositely charged or the electrons in one attracting those in the other. Each wire is neutral overall. The current in each wire makes a magnetic field, and that field pushes on the moving carriers in the other wire. Same-direction currents attract and opposite-direction currents repel.
How it runs
Students use one shared link and need no logins.
22 questions, about 30 minutes, no calculator required, single sitting.
The report arrives within 48 hours of your class finishing.
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Arons and Knight document the misconceptions. Moore and Chabay & Sherwood supply the physics treatment.