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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.

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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

Why it behaves this way

Explanation

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.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
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.

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Frozen valuesFrozen at 0.00

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?

Make a prediction before you reveal the next step.

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

Check your reasoning against the live bench.

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?

Use the live bench to test the result before moving on.

Accessibility

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.