Physics · Magnetism

Magnetic Fields

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What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Faraday's Law and Lenz's LawTurn changing magnetic fields into emf

Key takeaway

Current sign sets clockwise or counterclockwise magnetic-field circulation around a wire.
Current size and distance set how strongly one wire contributes at the probe.
The net magnetic field is the vector sum of both local tangent contributions, so symmetry can create reinforcement or cancellation.

Common misconception

The magnetic field points along the current-carrying wire or cancels whenever the two currents have equal size.

For a long straight wire, the magnetic field circles around the wire. At any point it is tangent to a circle centered on the wire, not parallel to the wire.

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Maxwell's Equations Synthesis

See what each Maxwell equation says physically, how sources and circulation differ, and why changing electric and magnetic fields together unify electricity, magnetism, and light.

Force from BMagnetism

Magnetic Force on Moving Charges and Currents

See why a magnetic field bends a moving charge sideways, why faster charges can make wider arcs, and how the same cross-product direction rule pushes a current-carrying wire.

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Equation snapshotCurrent sets circulation sense · Field from one long straight wireShow 3 equations

Current sets circulation sense
$I > 0 \Rightarrow B circles CCW, I < 0 \Rightarrow B circles CW$
In this model, positive current means out of the page and negative current means into the page, so the right-hand rule sets counterclockwise or clockwise circulation.
Field from one long straight wire
$B_{i} = k \frac{I _{i}}{r _{i}^{2}} (- Δ y_{i}, Δ x_{i})$
Each wire contributes a tangent magnetic field around itself. Current sign sets the circulation sense, and the field stays perpendicular to the radial line from the wire to the probe.
Net field by superposition
$B_{net} = B_{A} + B_{B}$
Add the two wire contributions at the same probe point to get the net magnetic field.

Why it behaves this way

Explanation

A magnetic field around a long straight wire does not point along the wire. It circles around the wire. Current direction sets the circulation sense through the right-hand rule, current size sets the field strength, and distance matters because the field gets weaker 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, scan graphs, worked examples, prediction prompts, and quick test, so the field pattern always stays tied to its sources.

Key ideas

01In this model, positive current means out of the page and gives counterclockwise magnetic circulation, while negative current means into the page and gives clockwise circulation.

02At the same distance from a wire, a larger current gives a larger magnetic field. At the same current, points farther from the wire have a weaker field.

03The net magnetic field at the probe comes from adding the two wire contributions at that same location.

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Frozen walkthrough

Use the current wire currents, spacing, and probe position directly from the stage. The same live values drive the probe arrows, the scan graphs, and the calculations below.

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Example 1 of 2

Frozen valuesUsing frozen parameters

Using the wire pair and probe position now on screen, what is the net magnetic field vector 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. Read the wire positions from the separation

With symmetric placement,

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

and

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

2. Form 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. Find each wire's 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 two contributions at the probe

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.

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