Skip to main content
ScienceVerse
PhysicsDifficulty 2-4

Magnetism

Magnetism is the push and pull between magnets, and between moving charges, carried by a magnetic field measured in teslas. Every magnet has a north and a south pole that cannot be separated; like poles repel and unlike poles attract. Electric currents create magnetic fields, and changing magnetic fields create currents — the link that powers generators and, together with electricity, explains light.

Sign in to save this concept.

Sources of Magnetic Field

Integrating the Biot–Savart law along an infinite straight wire gives a field that circles the wire and falls off as 1/R. Applying Ampère's law to a long solenoid gives a uniform interior field proportional to the turns per unit length.

Bwire=μ0I2πR,Bsolenoid=μ0nIB_{\text{wire}} = \dfrac{\mu_0 I}{2\pi R}, \qquad B_{\text{solenoid}} = \mu_0 n I

Long straight wire (left) and the interior of a long solenoid (right).

With μ₀ = 1.25663706127 × 10⁻⁶ N A⁻² (CODATA 2022), 10 A at 5.0 cm gives B ≈ 4.0 × 10⁻⁵ T. The vector force on a moving charge is F = qv × B; because F ⟂ v, F·v = 0 and the field does no work.

ε=−NdΦmdt,Φm=∫SB⋅n^ dA\varepsilon = -N\dfrac{d\Phi_m}{dt}, \qquad \Phi_m = \int_S \mathbf{B}\cdot\hat{\mathbf{n}}\,dA

Faraday's law with magnetic flux defined as the surface integral of B.

Info: Lenz's law is energy conservation in disguise: pushing a magnet into a coil, you work against the field of the induced current, and that work becomes the current's electrical energy.
Full explanation — the complete reference version every reading depth is based on

Magnets and poles

  • Every magnet has two poles, north (N) and south (S). Like poles repel; unlike poles attract; either pole attracts unmagnetised iron.
  • You cannot get a lone pole: cut a bar magnet in half and each half is a complete magnet with its own N and S.
  • Magnetic field lines show the field's direction (from N to S outside a magnet) and strength (closer lines, stronger field). They never cross and always form closed loops.
  • Earth acts like a giant bar magnet. The magnetic pole near the geographic North Pole is in fact a south magnetic pole — which is exactly why the north end of a compass needle swings towards it.

Currents make magnetic fields

In 1820 Hans Christian Oersted reported that a compass needle moved whenever current flowed in a nearby wire: an electric current produces a magnetic effect, and moving charges create magnetic fields. Around a long straight wire the field lines are circles centred on the wire, and the field weakens with distance.

B=μ0I2πRB = \dfrac{\mu_0 I}{2\pi R}

Magnetic field a distance R from a long straight wire carrying current I.

Worked example: a wire and a compass

Worked example (our calculation): with μ₀ ≈ 1.2566 × 10⁻⁶ N A⁻², a wire carrying 10 A produces B = (1.2566 × 10⁻⁶ × 10)/(2π × 0.05) ≈ 4.0 × 10⁻⁵ T = 40 μT at 5 cm. That is comparable to Earth's own field (about 22–67 μT at the surface), which is why a nearby current visibly turns a compass. Winding wire into a coil (a solenoid) concentrates the field: inside a long solenoid B = μ₀nI, uniform across the interior.

Forces on moving charges

F=qvBsin⁡θF = qvB\sin\theta

Magnetic force on a charge q moving at speed v at angle θ to a field B. 1 T = 1 N/(A·m).

The force is always at right angles to the charge's velocity, so it bends the path without speeding the charge up or slowing it down — the magnetic force does no work. A charge moving straight along the field lines (θ = 0) feels no force at all.

Changing fields make currents

From 1831 Michael Faraday showed the reverse effect: a changing magnetic field through a coil induces an emf. The faster the magnetic flux Φ changes, and the more turns N, the larger the emf. Lenz's law gives the direction: the induced current always opposes the change that caused it, as energy conservation demands. Generators use exactly this, rotating coils in magnetic fields.

ε=−NdΦdt\varepsilon = -N\dfrac{d\Phi}{dt}

Faraday's law of induction; the minus sign expresses Lenz's law.

Magnetic materials and Earth's field

Iron and its alloys are ferromagnetic: they contain tiny regions called domains in which atomic magnets are lined up. In an unmagnetised piece the domains point every which way; a strong field can line them up. Earth's own field is generated in its fluid outer core by a self-sustaining dynamo of currents in moving molten iron, and rocks record that its polarity has reversed many times, slowly and irregularly.

  • Earth's field at the surface: about 22,000–67,000 nT (22–67 μT), often rounded to 5 × 10⁻⁵ T.
  • The strongest permanent magnets: near 2 T.
  • Superconducting electromagnets: 10 T or more.

Where magnetism connects

Magnetism builds on Electricity (currents are its source) and Forces (F = qvB sin θ is a force like any other). Gravity, by contrast, is always attractive (see Gravity). Maxwell's unification of electricity and magnetism predicted electromagnetic waves travelling at c = 1/√(ε₀μ₀) — the explanation of Light.

How we know

  • Oersted's 1820 report of a compass needle moving whenever current flowed in a nearby wire showed that an electric current has a magnetic effect.
  • Faraday's experiments with changing magnetic fields, from 1831, established electromagnetic induction.
  • Geomagnetic observatories record accurate measurements of Earth's field direction and strength, continuously, over many years.
  • The magnetisation locked into rocks from many sites around the world records the direction of Earth's past field — the evidence for its reversals.
Common misconception: Misconception: Earth's 'North Magnetic Pole' must be a north magnetic pole. Opposites attract, so the pole that pulls the north end of a compass towards it must be a south magnetic pole. The name describes where it is, not its polarity.
Common misconception: Misconception: magnets attract all metals. Magnets strongly attract ferromagnetic materials such as iron. Aluminium (paramagnetic) and copper (diamagnetic) respond so weakly — their magnetic susceptibilities are only about 2.2 × 10⁻⁵ and −9.7 × 10⁻⁶ — that a fridge magnet will not stick to them.
Info: Assumptions and limits: B = μ₀I/(2πR) is exact only for an infinitely long, thin, straight wire, and B = μ₀nI only for the middle of a long solenoid, away from its ends. Earth's field is not a perfect bar magnet's either: its strength varies from place to place (about 22–67 μT) and it changes slowly over time. Strongly magnetic behaviour is a property of ferromagnetic materials such as iron; most other materials respond only very weakly.

Ask ScienceVerse

Still curious about Magnetism? Ask a question, get hints, take a short lesson or try a challenge. The tutor answers only from this concept's approved sources, and says so when it has none.

Ask the tutor about this concept on the full tutor page.

Connections

Prerequisites

Understand these first:

Guided learning path

See everything to learn before this, in order, with your progress:

Related concepts

Check your understanding

Take a quick check of two to five questions, with an explanation for every answer:

See the neighbourhood of Magnetism in the Knowledge Galaxy

Sources and methodology

Claims marked “awaiting scientific review” cite the sources listed but have not yet been signed off by a scientific reviewer.

Content status: published 1 October 2026.

  • Scientific review: this version has not yet been signed off by a scientific reviewer.
  • The Advanced explanation has not yet been reviewed for age suitability.