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CED objectives

Magnetism and Moving Charges

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletMoving Charge Bench · aim the velocity at any angle to the field, commit to the force direction, then run an orbit and check the energy

The magnetic force on a moving charge is $F = qvB\sin\theta$, so it vanishes for a charge at rest and for one moving along the field lines, and only the component of velocity perpendicular to $\vec{B}$ contributes. Its direction is perpendicular to both the velocity and the field, given by the right-hand rule for a positive charge and reversed for a negative one. Being always perpendicular to the velocity, it does no work, so the speed is unchanged and only the direction turns. For perpendicular entry into a uniform field the path is a circle of radius $r = mv/(qB)$, with period independent of speed.

Five errors dominate. Expecting a force on a charge that is at rest or moving parallel to the field, carried over from the electric case where the field acts regardless of motion. Drawing the force along the field or along the velocity, when it is perpendicular to both. Running the right-hand rule for a negative charge and reporting the result without the reversal. Letting the magnetic force raise the kinetic energy, when a perpendicular force does no work. And predicting a tighter circle for a faster particle, when $r = mv/(qB)$ makes the radius grow with speed.

check the velocity before anything else B into the page throughout × × × × × × × × × × × × × × at rest: v = 0 F = 0 v INTO the page, along B: sin0 = 0, F = 0 × F v ACROSS B: F = qvB, and F is perpendicular to both for a negative charge every yellow arrow reverses, and only the direction reverses
Two of the three charges sit in the same field and feel nothing. Only the component of velocity across the field produces anything at all.
r = mv/(qB): faster means a BIGGER circle v 2v same m, q, B qvB supplies mv²/r the force grows as v the requirement grows as v² so the circle has to OPEN UP T = 2πm/(qB): no v in it both particles go round in the same time “faster means a bigger force, so a tighter circle” stops at the first of the two powers of v
Both quantities in the balance grow with speed, and one of them grows faster. Solving for r first is what makes the direction of the effect unambiguous.

The work

3 ways in · any order
Lesson
Magnetism and Moving Charges ›

Requires velocity across the field before there is any force, puts the force perpendicular to both inputs with the sign reversal for a negative charge, and derives the radius rather than arguing from the force.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the failure modes of this topic: expecting a force on a stationary or field-parallel charge, drawing the force along the field or the velocity, skipping the reversal for a negative charge, letting the field change the speed, and shrinking the orbit of a faster particle. Take it cold to find which one is yours, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.

Take the diagnostic to identify your misconceptions
Diagnostic first