When a current flows through a long straight wire, it creates a magnetic field that circles the wire. Imagine the wire as a spinning wheel and the field lines as the spokes that go around it. The direction of the field is given by the right‑hand rule:
The field strength decreases with distance from the wire:
| Formula | Variables |
|---|---|
| \$B = \dfrac{\mu_0 I}{2\pi r}\$ | \$I\$ = current (A), \$r\$ = distance from wire (m) |
🔁 The field lines form concentric circles around the wire.
A flat circular coil is like a tiny loop of wire. When current flows, the coil behaves like a tiny magnet. The field is strongest at the centre of the coil.
At the centre of a single‑turn coil:
| Formula | Variables |
|---|---|
| \$B = \dfrac{\mu_0 I}{2R}\$ | \$R\$ = radius of coil (m) |
| \$B = \dfrac{\mu_0 N I}{2R}\$ | \$N\$ = number of turns |
🔄 The field lines run straight through the centre and loop back outside the coil.
A solenoid is a coil wound tightly like a spring. Inside a long solenoid the field is uniform and very strong.
Inside the solenoid:
| Formula | Variables |
|---|---|
| \$B = \mu_0 n I\$ | \$n\$ = turns per metre (m⁻¹) |
🔺 The field lines inside are straight and parallel, like the lines of a magnet.
| Tip | Why It Matters |
|---|---|
| Use the right‑hand rule first. | It prevents sign errors in the direction of \$B\$. |
| Remember \$B\$ decreases as \$1/r\$ for a straight wire. | Useful for questions about distance effects. |
| For a solenoid, \$B\$ is independent of \$r\$ inside. | Shows the advantage of many turns. |
| Concept | Formula |
|---|---|
| Straight wire | \$B = \dfrac{\mu_0 I}{2\pi r}\$ |
| Flat coil centre | \$B = \dfrac{\mu_0 N I}{2R}\$ |
| Long solenoid | \$B = \mu_0 n I\$ |