Electromagnets
A coil with 200 turns in 10 cm carrying 2 A makes a field of about 5 mT inside, about 100 times Earth's.
A current makes a magnetic field
In 1820 the Danish scientist Hans Christian Oersted noticed that a compass needle moved when a current flowed in a nearby wire. It was the first clear sign that electricity and magnetism are linked. Map the field around a long straight wire with compasses and the lines turn out to be circles around the wire. Their direction follows what OpenStax calls right hand rule 2: point your right thumb along the current, and your fingers curl the way the field goes round.
The strength falls off with distance: B = μ₀ I ÷ (2π r), where r is the distance from the wire. The constant μ₀ is the permeability of free space. Textbooks write it as 4π × 10⁻⁷ T·m/A; NIST's current value is 1.25663706127 × 10⁻⁶ N/A², which agrees with it to better than one part in a billion. OpenStax asks how much current gives twice Earth's field, 1.0 × 10⁻⁴ T, at 5.0 cm from a wire. The answer is I = 2π r B ÷ μ₀ = 25 A. Surveyors know this effect well: overhead power lines can throw their compass readings off.
Coils make strong, even fields
Bend the wire into a loop and the fields from every part of it add up in the middle. Wind many loops into a long coil, a solenoid, and the field inside becomes strong and nearly uniform, while the field just outside the turns is close to zero. Inside a long solenoid, B = μ₀ n I, where n is the number of turns per metre, N ÷ L. More turns packed into the same length, or more current, give a stronger field. Outside, the solenoid's field has the same shape as a bar magnet's, with a north and a south end.
Which end is north? Curl the fingers of your right hand round the coil the way the current flows in the turns; your thumb then points to the north end. Reverse the current and the poles swap. The lab coil is 10 cm long. With 200 turns and 2 A, n = 2,000 per metre and B = 1.2566 × 10⁻⁶ × 2,000 × 2 = 5.03 × 10⁻³ T, about 5 mT, roughly 100 times the 50 μT used for Earth's field. OpenStax's large example is a 2.00 m solenoid with 2,000 loops carrying 1,600 A: n = 1,000 per metre and B = 2.01 T, the strength of an MRI magnet. Such a current would overheat ordinary copper, which is why MRI machines use superconducting coils.
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Iron cores and what electromagnets do
Put an iron core inside the coil and the field from the current lines up the iron's domains, so the iron becomes a magnet too and adds its field to the coil's. Whenever strong magnetic effects are needed, electromagnets are given ferromagnetic cores. Unlike a permanent magnet, an electromagnet can be switched off, turned up or reversed. Scrapyard cranes lift cars with them and drop them by cutting the current. Particle accelerators steer beams with them, and MRI scanners hold patients inside a large superconducting coil. Coil resistance sets a limit: too much current and the wire overheats.
| Oersted, 1820 | A current moves a compass needle |
| Field of a long straight wire | B = μ₀ I ÷ (2π r), circles round the wire |
| Field inside a solenoid | B = μ₀ n I, n = turns per metre |
| μ₀ | 4π × 10⁻⁷ T·m/A ≈ 1.2566 × 10⁻⁶ |
| Which end of a coil is N? | Right fingers along the current, thumb points to N |
- A current makes a magnetic field (Oersted, 1820).
- Around a long straight wire the field lines are circles; B = μ₀ I ÷ (2π r).
- Inside a solenoid B = μ₀ n I; more turns per metre or more current, more field.
- The right-hand grip rule gives the N end; reversing the current swaps the poles.
- An iron core makes an electromagnet much stronger.
- Who first saw a current deflect a compass needle, in 1820?
- Hans Christian Oersted
- Michael Faraday
- William Gilbert
- Isaac Newton
- The field lines around a long straight wire are:
- Circles around the wire
- Straight lines along the wire
- Straight lines away from the wire
- There is no field
- Field 5.0 cm from a long wire carrying 25 A, in units of 10⁻⁴ T? (μ₀ = 4π × 10⁻⁷)
- Lab coil: 200 turns, 0.10 m long, 2 A. Field inside in mT? (two decimals)
- Turns per metre for 2,000 loops over 2.00 m?
- That solenoid carries 1,600 A. Field inside in tesla? (two decimals)
- You double both the turns and the current of a solenoid of fixed length. The field becomes:
- 4 times as strong
- 2 times as strong
- The same
- 8 times as strong
- You reverse the current in an electromagnet. What happens?
- The N and S ends swap
- It stops being a magnet
- It gets twice as strong
- Nothing changes
- Why do scrapyard cranes use electromagnets rather than permanent magnets?
- They can be switched off to drop the load
- They are lighter than air
- They attract aluminium
- They need no electricity
- Adding an iron core to a coil:
- Makes the field much stronger
- Cancels the field
- Reverses the poles
- Stops the current
Sources for this course (16)
- OpenStax College Physics 2e (openstax.org/books/college-physics-2e): 22.1 Magnets (all magnets have N and S poles, north-seeking and south-seeking, like poles repel and unlike attract, poles cannot be separated, the magnetic pole near the geographic North Pole is a south magnetic pole, sunspots come in N/S pairs)
- 22.2 Ferromagnets and electromagnets (iron, cobalt, nickel, gadolinium; neodymium alloys; domains grow to millimetre size; Curie temperature of iron 1043 K (770 °C); Oersted saw a compass needle deflected by a current; electromagnets in scrapyard cranes, particle accelerators and MRI; electric current is the source of all magnetism; no monopoles observed)
- 22.3 Magnetic fields and field lines (direction = where a compass north end points; four rules: tangent, density = strength, never cross, closed loops from N to S outside)
- 22.7 Magnetic force on a current-carrying conductor (F = I l B sin θ, 1 T = 1 N/(A·m), example 20.0 A, 5.00 cm, 1.50 T gives 1.50 N; motors)
- 22.9 Magnetic fields produced by currents (Oersted 1820, right hand rule 2, B = μ0 I ÷ (2π r), μ0 = 4π × 10⁻⁷ T·m/A, Earth's field about 5.0 × 10⁻⁵ T, 25 A at 5.0 cm gives twice that; loop centre B = N μ0 I ÷ 2R; solenoid B = μ0 n I, 2000 loops over 2.00 m with 1600 A gives 2.01 T, MRI; ferromagnetic cores)
- 23.1 Induced emf and magnetic flux (Faraday's iron-ring apparatus, emf only while the field changes, magnet pushed into a coil, faster motion gives more emf, generators, Φ = B A cos θ)
- NIST CODATA 2022 vacuum magnetic permeability μ0 = 1.25663706127(20) × 10⁻⁶ N/A² (physics.nist.gov/cgi-bin/cuu/Value?mu0)
- NOAA NCEI Geomagnetism Frequently Asked Questions (ncei.noaa.gov/products/geomagnetism-frequently-asked-questions): field like a dipole at Earth's centre, over 90% from the outer core, intensity roughly 25,000 to 65,000 nT (0.25 to 0.65 gauss)
- 1 gauss = 100,000 nT, declination = angle between magnetic north and true north (east positive)
- inclination, dip poles, dipole axis 9.41° from the rotation axis (WMM2020, 2020.0)
- north magnetic pole moving about 55 km per year north-northwest (2001 and 2007 surveys)
- last reversal about 750,000 to 780,000 years ago, reversals spaced 5 thousand to 50 million years, a reversal would take several thousand years, models renewed every five years, blackout zones where H < 2000 nT, compass balance weights differ by hemisphere, true bearing = magnetic bearing + declination
- NOAA NCEI news "World Magnetic Model 2025 Released" (17 December 2024)
- NOAA NCEI "December 2025 State of the Geomagnetic Field" (north dip pole 36 km/yr and south dip pole 9 km/yr since 1 January 2025)
- USGS, "Pre-gilbertian conceptions of terrestrial magnetism" (pubs.usgs.gov/publication/70009843): Gilbert's De Magnete (1600) first suggested that Earth behaves as a great magnet. Royal Institution, Michael Faraday's ring-coil apparatus (rigb.org): made August 1831, success on 29 August 1831, the first electric transformer
- APS News "This Month in Physics History" (Aug 2001): Faraday's electromagnetic rotation experiments of September 1821, the principle behind the electric motor.
Checked: 2026-10-17