Electric and magnetic fields in plain words

TL;DR:

• A field says what force a small test object would feel at each point in space. Electric field: force per charge, E = F/q, in N/C. Magnetic field: measured in tesla.

• Field lines show direction by their arrows and strength by how close together they are.

• A current makes a magnetic field that circles the wire. The right-hand rule gives the direction, and a long straight wire gives B = μ₀I / 2πr.

A compass needle lies still, pointing roughly north. Lay a wire next to it, run a current through, and the needle swings. Nothing touched it. Something in the space around the wire pushed it, and physicists call that something a field.

What a field is

A field assigns a value to every point in space. The electric field tells you what force a small positive test charge would feel there. In symbols, E = F / q, so its unit is newtons per coulomb (N/C), which is the same as volts per metre.

A single point charge Q makes a field of size E = kQ / r², where k ≈ 8.99 × 10⁹ N·m²/C². It points away from a positive charge and toward a negative one, and it weakens with the square of the distance.

Magnetic fields come from moving charges, which means currents, and from the tiny currents inside magnets. The strength is written B and measured in tesla (T). One tesla is a large field, so everyday fields are quoted in microtesla (μT).

Reading field lines

Field lines are a drawing tool. The arrow shows which way the field points, and the spacing shows strength: lines close together mean a strong field, lines far apart mean a weak one. Electric field lines start on positive charges and end on negative ones.

Magnetic field lines have no start or end. They form closed loops, running out of a magnet's north pole and back in at the south pole, and continuing through the inside of the magnet. A compass needle's north end points along the local field.

The right-hand rule for a wire

A straight wire with current makes magnetic field lines that form circles around it. To find the direction, point the thumb of your right hand along the conventional current (the direction positive charge would flow). Your fingers curl the way the field circulates.

For a long straight wire the strength at distance r is B = μ₀ I / (2π r), with μ₀ = 4π × 10⁻⁷ T·m/A. Double the current and the field doubles. Double the distance and it halves.

Worked example: a compass needle near a wire

Lay a long straight wire along the north-south line, with the compass 5 cm directly below it. Say 2 A flows through the wire toward the north. Say also that the horizontal part of Earth's field at your spot is 20 μT. That is a made-up value in the typical range, so check a local value if you need one.

1. Field from the wire: B = μ₀I / 2πr = (4π × 10⁻⁷ × 2) / (2π × 0.05). The π cancels: = (2 × 10⁻⁷ × 2) / 0.05 = 4 × 10⁻⁷ / 0.05 = 8 × 10⁻⁶ T, which is 8 μT.

2. Direction: thumb points north. At a spot below the wire, the fingers curl so the field points west. (Above the wire it would point east.)

3. Combine: Earth's field is 20 μT toward the north and the wire's is 8 μT toward the west. They are at right angles, so the needle settles along the sum.

4. Deflection angle: tan θ = 8 / 20 = 0.4, so θ ≈ 22° from north toward the west.

That is Oersted's discovery in numbers: a current deflects a compass, so electricity and magnetism are linked. Reverse the current and the needle swings 22° the other way. Turn the current off and it goes back to north.

Do not short a battery: A real experiment needs a bulb or resistor in the loop. A bare wire across a battery draws a very large current, so the wire and battery can get hot enough to burn you or start a fire. Use a small battery, keep the loop short and break the connection if anything warms up.

How to check your answer

• Units. T·m/A × A / m = T. The metres cancel and amps cancel.

• Scale. Wire fields at centimetres from a few amps are microtesla, a bit smaller than Earth's field, so a visible but partial turn is sensible. A turn of 90° would need the wire's field to be much larger than Earth's.

• Direction by symmetry. Reverse the current and the deflection should flip sides. If your answer does not, recheck the right-hand rule.

• Limits. tan θ is 0 when the wire's field is zero, so the needle must point north then.

Mistakes to avoid

• Using your left hand, or pointing the thumb along the electron flow instead of the conventional current.

• Thinking field lines are physical objects. They are a map, and the field exists between the lines too.

• Adding fields as plain numbers. Fields are vectors, so directions matter, and perpendicular fields combine with Pythagoras.

• Mixing up units: N/C for electric field, T for magnetic.

• Forgetting to convert centimetres to metres before using the formula.

Where you will use it next

Fields lead to motors, generators and radio. A changing field makes the other kind, which is how light and radio travel through empty space, covered in how waves carry energy. The idea of potential difference behind the electric field appears in what voltage actually is.

Frequently asked questions

Is a magnetic field the same as an electric field?

No. They are different fields, but they are linked: moving charges make magnetic fields, and changing magnetic fields make electric ones.

Why do field lines get closer near a pole?

The same field loops are squeezed into a smaller area, so the field is stronger there.