Physics · Magnetism

Magnetic Force on Moving Charges and Currents

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Uniform Circular MotionCurved-motion comparison

Key takeaway

In this module the charge velocity is perpendicular to the magnetic field, so |F_q| = |q|vB and the force lies in the page at right angles to the velocity.
Because the magnetic force is perpendicular to the motion, it changes direction without directly changing speed; a velocity parallel to the field would not curve in this simplified setup.

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 directly changing the speed.

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Curved-motion comparisonMechanics

Uniform Circular Motion

Track a particle moving at constant speed around a circle and connect radius, angular speed, tangential speed, centripetal acceleration, and the inward-force requirement to the same live state.

Force-field contrastElectricity

Electric Fields

See how source-charge sign, distance, and superposition set the electric field at one probe, then watch a test charge turn that field into a force without changing the field itself.

Reconnect current to sourceCircuits

Basic Circuits

Keep one battery and two resistors in view while current, voltage, resistance, Ohm's law, and the contrast between series and parallel all stay tied to one honest circuit.

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Reference and support

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Equation snapshotMagnetic force on a moving charge · Perpendicular-force magnitudeShow 2 equations

Magnetic force on a moving charge
$F_{q} = q v \times B$
The direction comes from the cross product, so the force is perpendicular to both the velocity and the magnetic field.
Perpendicular-force magnitude
$∣ F_{q} ∣ = ∣ q ∣ v B$
In this module the velocity stays perpendicular to the field, so the force size is set by |q|, speed, and field strength.

Why it behaves this way

Explanation

A magnetic field does not push a resting charge, and it does not push a moving charge along the field the way an electric field can. In this lab the velocity lies in the page and the field points into or out of the page, so q v x B is sideways to the motion.

That sideways force changes heading rather than directly changing speed. Use the force arrow, orbit guide, and force graph together: |F_q| grows with speed and field strength, while r = mv / (|q|B) explains why a faster charge can trace a wider arc.

The same stage also shows a 1 m current segment using I L x B. A charge-sign flip reverses only q v x B, but a field flip reverses both the moving-charge force and the wire force.

Key ideas

01In this module the charge velocity is perpendicular to the magnetic field, so |F_q| = |q|vB and the force lies in the page at right angles to the velocity.

02Because the magnetic force is perpendicular to the motion, it changes direction without directly changing speed; a velocity parallel to the field would not curve in this simplified setup.

03Flipping either the charge sign or the magnetic-field direction reverses the moving-charge force. Flipping both together restores the original bend direction.

04At fixed field, increasing speed makes the magnetic force larger but also makes the circular path radius larger, because the faster charge is harder to turn.

05A current segment uses I L x B. If the segment points the same way as a positive moving charge, it gives the same force side.

Worked examples

Work from the live state

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the current field sense, charge sign, direction angle, and speed directly from the stage. The charge path, wire-force panel, graphs, and orbit guide all read the same live setup.

Supporter unlocks saved study tools, exact-state sharing, and the richer review surfaces that support this guided flow.

View plans

Example 1 of 2

Frozen valuesFrozen at 0.00

For the current moving charge, what magnetic force acts now, and what turning radius follows from that state?

q

Charge sign

positive

B

Field strength

1.6 T

v

Charge speed

4.5 m/s

θ

In-page direction

0 °

1. Set the force direction from the positive-charge 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 the force magnitude

∣ F_{q} ∣ = ∣ q ∣ v B = 4.5 \times 1.6 = 7.2

in the normalized live model.

3. Convert that same state into the turning radius

r = \frac{v}{∣ B ∣} = \frac{4.5}{1.6} = 2.81 m

, so the path curves clockwise.

Charge force and radius

F_{q} = (0, - 7.2), ∣ F_{q} ∣ = 7.2, r = 2.81 m

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

Quick test

Loading saved test state.

Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

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.

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Starter track

Step 3 of 3

Magnetism

Magnetic Force on Moving Charges and Currents appears later in this track, so it is cleaner to start from the beginning first.

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

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