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Concept module

Magnetic Force on Moving Charges and Currents

Launch one moving charge through a uniform magnetic field, compare it with a same-direction current segment, and connect force direction, curvature, and current-based force on one bounded live stage.

The simulation shows a square stage with x and y axes, a launch point at the center, a draggable launch handle, a moving charge that follows a curved path through a uniform magnetic field, and a compact wire-force panel to the right. Dots indicate magnetic field out of the page, crosses indicate magnetic field into the page, and a gray hollow marker indicates nearly zero field. The moving charge uses color to show sign: warm color for positive and cool color for negative. Optional overlays show field markers, the live velocity and force arrows on the charge, the orbit guide and orbit center, and the current-segment panel with its own force arrow. The right panel uses the same in-page direction angle as the launch arrow but a separate current slider. Compare mode can add a dashed secondary path and secondary wire segment while the time rail, graph hover, and pause controls still inspect one synchronized time value. At t = 0 s, a positive charge moving at 4.5 m/s in 1.6 T out of the page has F_q = (0, -7.2), so the charge force points down with a radius of about 2.81 m. The matching wire segment force points down with magnitude 3.2. The positive charge and same-direction current segment point to the same force side in this uniform field.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 2.16 sLivePause to inspect a specific moment, then step or scrub through it.
0.00 s2.16 s

Magnetic Force on Moving Charges and Currents

Drag the launch handle to change the shared direction and speed. The charge motion uses one normalized moving charge in a uniform field, while the wire panel reuses the same direction with a 1 m current segment.

-8-4048-8-448xyB out of the pagecentervF_qlaunchq+drag v0Live readoutB+1.6 Tq+1|v|4.5 m/stheta0 deg|F_q|7.2r2.81 mI2 A|F_wire|3.2Field: out of the pageCharge force: downPositive charge and current share the same force direction.Current segmentSame direction control, separate I sliderIF_wireq+ matches the wire-force side.preview window: 3.2 s

Graphs

Switch graph views without breaking the live stage and time link.

Charge position vs time

Tracks the charge coordinates while the stage shows the same moving point and orbit guide.

Time (s): 0 to 3.2Position (m): -8 to 8
Charge xCharge y
Charge position vs timeTracks the charge coordinates while the stage shows the same moving point and orbit guide.00.81.62.43.2-8-4048Time (s)Position (m)
Hover or scrub to link the graph back to the stage.Time (s) / Position (m)

Controls

Adjust the physical parameters and watch the motion respond.

1.6 T

Positive values mean the field points out of the page and negative values mean into the page.

4.5 m/s

Sets the charge speed before the magnetic field bends the path.

0°

Rotates the shared launch or current direction inside the page.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show
2 A

Scales the current-segment force in the comparison panel.

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 1
With a positive charge and an out-of-page field, a rightward launch bends downward. The wire panel points to that same side because it uses the positive-charge current rule.

Try this

Start from Positive bends down, then toggle Negative charge without changing any other control.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

Field strength
1.6 T

Sets the size and sign of the uniform magnetic field. Positive means out of the page and negative means into the page.

Graph: Charge position vs timeGraph: Magnetic force vs timeOverlay: Field markersOverlay: Charge vectorsOverlay: Orbit guideOverlay: Wire-force panel

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use these prompts to read the same force story from the stage, wire panel, and graphs before you reach for a memorized hand rule.

ObservationPrompt 1 of 1
With a positive charge and an out-of-page field, a rightward launch bends downward. The wire panel points to that same side because it uses the positive-charge current rule.

Try this

Start from Positive bends down, then toggle Negative charge without changing any other control.

Why it matters

This is the clean baseline that makes later sign flips feel deduced rather than guessed.
Control: Field strengthControl: In-page directionControl: Negative chargeGraph: Magnetic force vs timeOverlay: Field markersOverlay: Charge vectorsOverlay: Wire-force panelEquationEquationEquation

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

4 visible

Overlay focus

Field markers

Shows the uniform magnetic-field sense across the stage with dots or crosses.

What to notice

  • Dots mark field out of the page, and crosses mark field into the page.

Why it matters

The field sense decides which side the right-hand rule should choose before the charge sign or current comparison is applied.

Control: Field strengthGraph: Magnetic force vs timeEquation

Challenge mode

Tune the same bounded field-and-force model into direction targets that force you to separate charge sign from current direction instead of leaning on a memorized rule.

0/2 solved
ConditionStretch

2 of 10 checks

Faster force, wider arc

Open compare mode from Positive bends down. Keep Setup A as the baseline, but make Setup B show the bigger moving-charge force and the wider orbit that go with a faster charge in the same field.
Compare modeGraph-linkedGuided start2 hints

Suggested start

Open compare mode from the baseline and raise only Setup B speed while keeping the orbit guide and wire panel visible.
Pending
Open the Magnetic force vs time graph.
Charge position vs time
Matched
Keep the Orbit guide visible.
On
Matched
Keep the Wire-force panel visible.
On
Pending
Stay in compare mode while editing Setup B.
Explore
Pending
Keep Setup A near the baseline moving-charge force of 7.2.
Pending
Keep Setup A on the baseline radius near 2.8 m.
Pending
Raise Setup B speed into the 6.2 to 6.6 m/s band.
Pending
Make Setup B's moving-charge force exceed 10.0.
Pending
Make Setup B's orbit widen to a radius near 4.0 m.
Pending
Keep Setup B's wire-panel force near 3.2 so only the moving-charge speed changed.

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

At t = 0 s, a positive charge moving at 4.5 m/s in 1.6 T out of the page has F_q = (0, -7.2), so the charge force points down with a radius of about 2.81 m. The matching wire segment force points down with magnitude 3.2. The positive charge and same-direction current segment point to the same force side in this uniform field.
Equation detailsDeeper interpretation, notes, and worked variable context.

Magnetic force on a moving charge

The direction comes from the cross product, so the force is perpendicular to both the velocity and the magnetic field.

Field strength 1.6 T Charge speed 4.5 m/s In-page direction 0° Charge sign Off

Perpendicular-force magnitude

Because the velocity stays perpendicular to the field in this module, the sine factor is 1 and the force scale is set by charge sign, speed, and field size.

Field strength 1.6 T Charge speed 4.5 m/s

Radius of curved motion

A stronger field tightens the path, while a faster charge widens the path in the same field.

The live charge motion uses normalized m = 1 and |q| = 1, so the stage radius scales like v / |B|.
Zero field means no finite magnetic radius because the path becomes straight.
Field strength 1.6 T Charge speed 4.5 m/s

Magnetic force on a current segment

A current-carrying wire segment in the field uses the same cross-product direction idea as the positive-charge case.

Field strength 1.6 T In-page direction 0° Wire current 2 A

One sign flip reverses the force

Changing the charge sign or the field direction by itself reverses the force direction. Changing both together restores the original side.

Field strength 1.6 T In-page direction 0° Charge sign Off

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Starter track

Step 3 of 30 / 3 complete

Magnetism

Earlier steps still set up Magnetic Force on Moving Charges and Currents.

1. Magnetic Fields2. Faraday's Law and Lenz's Law3. Magnetic Force on Moving Charges and Currents

Previous step: Faraday's Law and Lenz's Law.

Start from track beginning

Short explanation

What the system is doing

A magnetic field does not push a resting charge along the field the way an electric field can. In this bounded model the field points perpendicular to the page, so a moving charge feels a sideways force given by q v x B. That force stays perpendicular to the velocity, so the speed can stay fixed while the direction keeps turning.

The same stage also shows a current-carrying wire segment pointing in the same in-page direction. That keeps the bridge to F = I L x B compact instead of turning into a giant electromagnetism engine: one shared field sense, one shared direction control, one moving charge, one current segment, and one set of graphs, prompts, worked examples, compare mode, and quick tests.

Key ideas

01For the moving charge in this module, the magnetic field is perpendicular to the page. The charge force is therefore sideways in the plane and always perpendicular to the velocity.
02Flipping either the charge sign or the magnetic-field direction reverses the moving-charge force. Flipping both together restores the original bend direction.
03At fixed magnetic field, increasing speed makes the magnetic force larger and also makes the circular path radius larger. Bigger force does not automatically mean tighter curvature here.
04A current segment uses I L x B. If the segment points the same way as a positive moving charge, the force direction matches the positive-charge case.

Live force checks

Solve the exact state on screen.

Solve both representations from the current live state. The charge motion, wire panel, force graph, and orbit guide all read the same field sign, direction angle, and control values.
Live valuesLive at t = 0.00 s

For the current moving charge, what magnetic force acts now, and what radius does that imply for the path?

Charge sign

positive

Field strength

1.6 T

Speed

4.5 m/s

Launch angle

0 °

1. Start from the positive-charge right-hand-rule baseline

The field is out of the page, so a positive charge launched at 0^\circ would feel a down magnetic force. Because this charge is positive, the actual force points down.

2. Use the live speed and field size for |F_q|

in the normalized live model.

3. Translate the same state into curvature

, so the path curves clockwise.

Charge force and radius

.
Because the charge is positive, the actual bend follows the standard right-hand-rule direction for the live launch arrow and field sense.

Charge-to-current checkpoint

If the magnetic field stays fixed, why can a faster charge feel a larger magnetic force and still trace a wider circle instead of a tighter one?

Prediction prompt

Decide what happens to both |F_q| and r before you raise the speed slider.

Check your reasoning

Because |F_q| grows with v, but the circular-motion radius also scales like v / |B|. A faster charge needs a larger turning radius even while the magnetic force magnitude increases.
The force is bigger because qvB is bigger, but the charge also has more momentum to redirect. In this uniform-field model the resulting radius grows with speed, so the orbit becomes wider rather than tighter.

Common misconception

A magnetic force must slow a charge down because it is always pushing on the charge.

In this ideal uniform-field setup the magnetic force is perpendicular to the velocity, so it changes direction without doing work on the charge. The speed can stay constant while the path curves.

What changes is the heading, not the kinetic-energy scale. That is why the force graph rotates through x and y components while the speed readout stays fixed.

Quick test

Reasoning

Question 1 of 4

Answer from force logic, not from a detached hand-rule chant. Each question asks what the live field, charge sign, speed, and current segment must imply together.

A positive charge moves to the right in a magnetic field pointing out of the page. Which way is the magnetic force in this model?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows a square stage with x and y axes, a launch point at the center, a draggable launch handle, a moving charge that follows a curved path through a uniform magnetic field, and a compact wire-force panel to the right. Dots indicate magnetic field out of the page, crosses indicate magnetic field into the page, and a gray hollow marker indicates nearly zero field.

The moving charge uses color to show sign: warm color for positive and cool color for negative. Optional overlays show field markers, the live velocity and force arrows on the charge, the orbit guide and orbit center, and the current-segment panel with its own force arrow.

The right panel uses the same in-page direction angle as the launch arrow but a separate current slider. Compare mode can add a dashed secondary path and secondary wire segment while the time rail, graph hover, and pause controls still inspect one synchronized time value.

Graph summary

The position graph plots the charge x-position and y-position against time for the current setup. Hovering or scrubbing the graph updates the same charge position on the stage.

The force graph plots the charge force x-component, charge force y-component, and charge force magnitude against the same time axis. The graph does not draw the wire force; the wire comparison stays in the live panel so the current-segment rule remains visually distinct from the moving-charge force.