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CED objectives

Magnetism and Current-Carrying Wires

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletTwo-Wire Bench · two wires through the page, a probe that halves its distance, and a wire that only partly crosses a band of field

The magnetic field of a long straight wire circles the wire, tangent to circles centred on it, with direction given by gripping the wire with the right hand and the thumb along the conventional current. Its magnitude is $B = \mu_0 I/(2\pi r)$, proportional to $I/r$, so halving the distance doubles the field rather than quadrupling it. Two parallel wires with current in the same direction attract and antiparallel currents repel, a result obtained by finding one wire's field at the other and then the force that field exerts on the second current. The force on a wire is $F = BIL\sin\theta$, with $L$ only the length inside the field.

Four errors dominate. Drawing a wire's field as spokes radiating outward, or laying it along the current, both of which import the electric picture of a charged rod. Scaling the field as inverse square, when a long wire's field spreads around a circle and costs only one power of $r$. Applying the like-repels rule to two wires carrying current in the same direction, when they attract. And using the whole length of a wire in $F = BIL\sin\theta$ when only part of it lies inside the field, or dropping the angle so that a wire parallel to the field is given a force.

grip the wire, thumb along the current, fingers curl the field I out of the page into the page B circles the wire no component toward it, away from it, or along it NOT this: spokes borrowed from a charged rod a field pointing the wrong way puts every downstream force in the wrong direction
The falloff is the same on both sides of this figure. What separates them is the direction, and that is what every force calculation downstream depends on.
chain two right-hand rules; do not match the charge pattern I I step 1: wire 1's B here points into the page same direction: ATTRACT step 2: an upward current in an into-page field is pushed left I I opposite directions: REPEL reverse one current and both steps flip once
The rule reverses the one for charges, so pattern-matching gets every two-wire problem backward. Running both steps is what makes the direction come out.

The work

3 ways in · any order
Lesson
Magnetism and Current-Carrying Wires ›

Circles the field around a wire rather than radiating it, scales it as one over r, derives the force between two wires by chaining the rules, and counts only the length inside the field.

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

Ten items spanning the failure modes of this topic: radiating a wire's field outward, using inverse-square falloff, applying the like-repels rule to parallel currents, and using the whole wire length or dropping the angle in the force. 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