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Concept module

Magnetic Fields

See how current direction, wire spacing, distance, and superposition set the magnetic field around one or two long straight wires, with the stage arrows and scan graphs tied to the same live source pattern.

Interactive lab

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

Magnetic Fields

Drag the probe anywhere in the stage or drag either wire marker to change the shared separation. Dot markers mean current out of the page and cross markers mean current into the page.

Graphs

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

Horizontal field scan

Shows how each wire contributes to B_x and how those contributions add along the current horizontal scan line.

probe x-position (m): -3.2 to 3.2horizontal magnetic-field component: -4 to 4

Wire A B_xWire B B_xNet B_x

Hover or scrub to link the graph back to the stage.probe x-position (m) / horizontal magnetic-field component

Controls

Adjust the physical parameters and watch the motion respond.

Wire A current

I_{A}

2 A

Positive values mean out of the page and negative values mean into the page, so changing the sign reverses Wire A's circulation sense.

Wire B current

I_{B}

-2 A

Changing Wire B lets the second swirl reinforce, cancel, or reverse the net magnetic field.

Wire separation

s

2.4 m

Moves both wires symmetrically along the horizontal axis without breaking the bounded layout.

Probe x-position

x_{p}

0 m

Moves the probe left or right across the stage and the linked scan graphs.

More tools

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

Hide

Probe y-position

y_{p}

1 m

Moves the probe to a new horizontal scan line so the graphs sample a different field slice.

More presets

Presets

Predict -> manipulate -> observe

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

Graph readingPrompt 1 of 3

The net scan curve is not a separate rule. It is the point-by-point sum of the amber and sky source curves on the same y-level.

Try this

Open the horizontal scan graph and move the probe along the dashed scan line. The probe marker and the graph preview should stay synchronized.

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.

I_{A}

Wire A current

2 A

Changes the size and sign of Wire A's current, which changes both the local field strength and whether its circulation is counterclockwise or clockwise.

Graph: Horizontal field scanGraph: Vertical direction and strengthOverlay: Field loopsOverlay: Field vectorsOverlay: Field grid

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 the current prompt as a compact investigation cue. Each one points at a magnetic-field pattern the stage and graphs already show in the live state.

Graph readingPrompt 1 of 3

Graph: Horizontal field scan

The net scan curve is not a separate rule. It is the point-by-point sum of the amber and sky source curves on the same y-level.

Try this

Open the horizontal scan graph and move the probe along the dashed scan line. The probe marker and the graph preview should stay synchronized.

Why it matters

It turns magnetic superposition into an observable graph relationship instead of a memorized slogan.

Control: Probe x-positionControl: Probe y-positionGraph: Horizontal field scanOverlay: Field vectorsOverlay: Graph scan line

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 loops

Shows circular guide loops around each wire to make the right-hand-rule pattern visible.

What to notice

Dot markers pair with counterclockwise loop arrows, while cross markers pair with clockwise loop arrows.

Why it matters

It ties the visible field pattern directly to the source instead of leaving current direction as an isolated rule.

Control: Wire A currentControl: Wire B currentGraph: Horizontal field scanGraph: Vertical direction and strengthEquation

I_{A}

Equation

I_{B}

Challenge mode

Tune the same two-wire stage into compact magnetic-field targets. The checklist reads the live superposition state instead of a detached answer key.

0/2 solved

TargetCore

6 of 7 checks

Build the upward magnetic field

Starting from Same-current sweep, reverse Wire B so the sideways contributions nearly cancel while the net magnetic field points strongly upward above the midpoint.

Graph-linkedGuided start2 hints

Suggested start

Use the direction scan and the probe vectors together while you tune the wire pair.

Pending

Open the Vertical direction and strength graph.

Horizontal field scan

Matched

Keep the Field vectors visible.

Matched

Keep the Graph scan line visible.

Matched

Keep current a between 1.9 A and 2.1 A.

2 A

Matched

Keep current b between -2.1 A and -1.9 A.

-2 A

Matched

Keep field x between -0.08 and 0.08.

Matched

Keep field y between 1.85 and 2.05.

1.97

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

At the probe (0 m, 1 m), currents 2 A and -2 A separated by 2.4 m produce B_x = 0 and B_y = 1.97, so the net magnetic field is 1.97 in field units and points up. The two wire senses compete, so the local net direction has to be read from vector addition.

Equation detailsDeeper interpretation, notes, and worked variable context.

Symmetric wire positions

The shared separation control places Wire A and Wire B equally far from the origin on the horizontal axis.

x_{A} = - \frac{s}{2}, x_{B} = + \frac{s}{2}

s

Wire separation 2.4 m

Current sets circulation sense

Positive current means out of the page in this model and negative current means into the page, so the right-hand rule chooses counterclockwise or clockwise circulation.

I > 0 \Rightarrow B circles CCW, I < 0 \Rightarrow B circles CW

I_{A}

Wire A current 2 A

I_{B}

Wire B current -2 A

Field from one long straight wire

Each wire contributes a tangential field whose circulation sense comes from current direction.

B_{i} = k \frac{I _{i}}{r _{i}^{2}} (- Δ y_{i}, Δ x_{i})

Changing the sign of I_i reverses the local tangent direction.

The field stays perpendicular to the radial line from the wire to the probe.

I_{A}

Wire A current 2 A

I_{B}

Wire B current -2 A

x_{p}

Probe x-position 0 m

y_{p}

Probe y-position 1 m

Field-strength trend

Doubling current doubles the field at the same point, while moving farther from the wire weakens the field.

∣ B ∣ \propto \frac{∣ I ∣}{r}

I_{A}

Wire A current 2 A

I_{B}

Wire B current -2 A

s

Wire separation 2.4 m

Superposition

The net magnetic field at one probe point is the vector sum of both wire contributions evaluated at that same location.

B_{net} = B_{A} + B_{B}

I_{A}

Wire A current 2 A

I_{B}

Wire B current -2 A

s

Wire separation 2.4 m

x_{p}

Probe x-position 0 m

y_{p}

Probe y-position 1 m

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 1 of 30 / 3 complete

Magnetism

Next after this: Faraday's Law and Lenz's Law.

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

This concept is the track start.

See next concept

Short explanation

What the system is doing

A magnetic field around a long straight wire circles the wire instead of pointing along it. Current direction sets the circulation sense through the right-hand rule, current size sets how strong that local swirl is, and distance still matters because the field weakens as you move farther from the wire.

This module keeps one bounded two-wire stage, one movable probe, and one linked scan line. The same current directions, current sizes, wire spacing, and probe position drive the field loops, probe vectors, worked examples, prediction prompts, quick test, and compare mode so magnetic-field patterns stay tied to their source instead of turning into a detached rule sheet.

Key ideas

01Positive current in this model means out of the page and produces a counterclockwise magnetic-field circulation. Negative current means into the page and produces a clockwise circulation.

02At one fixed distance from a wire, stronger current gives a stronger magnetic field. At one fixed current, moving farther away weakens the field.

03The net magnetic field at the probe is the vector sum of both wire contributions evaluated at that same location.

Live magnetic checks

Solve the exact state on screen.

Solve the current probe state directly from the live controls. The same wire currents, spacing, and probe point now on screen determine the stage arrows, scan graphs, and explanations below.

Live valuesFollowing current parameters

For the current wire pair and probe point, what net magnetic field vector acts at the probe?

I_{A}

Wire A current

2 A

I_{B}

Wire B current

-2 A

s

Wire separation

2.4 m

x_{p}

Probe x-position

0 m

y_{p}

Probe y-position

1 m

1. Place the two wires on the shared axis

With symmetric placement,

x_{A} = - s /2 = - 1.2 m

and

x_{B} = + s /2 = 1.2 m

2. Build the wire-to-probe position vectors

r_{A} = (1.2, 1)

with

∣ r_{A} ∣ = 1.56

, and

r_{B} = (- 1.2, 1)

with

∣ r_{B} ∣ = 1.56

3. Evaluate each tangential magnetic-field contribution

B_{A} = I_{A} (- Δ y_{A}, Δ x_{A}) / r_{A}^{2} = (- 0.82, 0.98)

and

B_{B} = I_{B} (- Δ y_{B}, Δ x_{B}) / r_{B}^{2} = (0.82, 0.98)

4. Add the vectors at the same probe point

B_{net} = B_{A} + B_{B} = (0, 1.97)

, so

∣ B ∣ = 1.97

Net magnetic field

B_{net} = (0, 1.97), ∣ B ∣ = 1.97

The two wire contributions are closely balanced here, so the final direction has to be read from careful vector addition.

Right-hand-rule checkpoint

Keep both currents equal and out of the page, then place the probe exactly halfway between the wires on the same horizontal axis. What must happen to the two magnetic-field contributions there, and why can the net field vanish even though each wire still makes a nonzero field on its own?

Prediction prompt

Predict which tangential directions oppose before you move the probe onto the midpoint.

Check your reasoning

The two contributions are equal in size and opposite in direction at that midpoint, so they cancel and the net field is zero there.

The midpoint sits the same distance from both wires, so equal currents create equal-magnitude fields there. Because the probe lies on the shared axis between the wires, the two tangential directions point opposite ways, and the vector sum vanishes.

Common misconception

If current goes to the right through a wire, the magnetic field near that wire also points to the right.

For a long straight wire, the magnetic field wraps around the wire in circles. It is tangent to those circles, not aligned with the wire itself.

Current direction matters because it chooses clockwise or counterclockwise circulation through the right-hand rule. The probe direction still depends on where the probe sits around the wire.

Quick test

Variable effect

Question 1 of 4

Answer from field logic, not from isolated mnemonics. Each question asks what the stage and graphs must mean about circulation sense, superposition, or field strength around current-carrying wires.

A probe sits to the right of one isolated wire. If the current changes from +2 A to -2 A at the same location, what must happen to the magnetic field at the probe?

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 two long straight wires on a horizontal axis, a movable probe inside a bounded magnetic-field region, and optional overlays for circular guide loops around each wire, a field-sample grid, source-contribution arrows, the net magnetic-field arrow at the probe, and the horizontal scan line used by the graphs.

A dot marker means current out of the page and a cross marker means current into the page. Dragging the probe changes the sampled field location directly on the stage, while dragging either wire marker changes the shared wire separation symmetrically. Sliders provide the same controls for current size and sign, separation, and probe position.

Very near a wire marker, the field display uses a minimum sampling radius so the drawn arrows stay finite and readable. This keeps the visualization bounded while still preserving the correct trend that magnetic field strength grows rapidly near a wire.

Graph summary

The horizontal field-scan graph plots Wire A's horizontal contribution, Wire B's horizontal contribution, and the net horizontal magnetic field along the current scan line. Hovering the graph previews the same x-location on the stage.

The direction-and-strength graph plots the net vertical component and the total magnetic-field strength along that same scan line. Both graphs remain field-only readouts generated by the wire currents and the current probe location.

Keep the source-field story moving

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Change flux into emfElectromagnetism

Magnetic Fields

See each variable before you move it.

Field loops

Build the upward magnetic field

Magnetism

What the system is doing

Solve the exact state on screen.

For the current wire pair and probe point, what net magnetic field vector acts at the probe?

A probe sits to the right of one isolated wire. If the current changes from +2 A to -2 A at the same location, what must happen to the magnetic field at the probe?

Keep moving through the concept map.

Faraday's Law and Lenz's Law

Maxwell's Equations Synthesis

Magnetic Force on Moving Charges and Currents