When an electric current flows through a straight wire, it creates a circular magnetic field around the wire. Imagine the wire as a spinning top: the field lines wrap around it like a whirlpool.
Mathematically, the magnetic field strength at a distance r from the wire is given by the Ampère–Coulomb law:
\$B = \dfrac{\mu_0 I}{2\pi r}\$
where I is the current, μ₀ is the permeability of free space (4π × 10⁻⁷ H/m), and r is the radial distance.
To find the direction of the magnetic field, use the Right‑Hand Rule:
🧲 Tip: Think of the wire as a magnet’s invisible hand, pulling the field lines around it.
A solenoid is a coil of wire. Inside a long solenoid, the magnetic field is almost uniform and points along the axis of the coil.
Formula for the magnetic field inside a solenoid:
\$B = \mu_0 n I\$
where n is the number of turns per unit length.
Outside the solenoid, the field is very weak, almost zero.
When you put a coil around a nail and connect it to a battery, the nail becomes a magnet. The current creates a magnetic field that aligns the iron atoms in the nail, turning it into a magnet.
🔌 Analogy: The coil is like a group of tiny spinning tops (current) that line up the magnetic “spins” inside the nail.
📝 Remember: In exam questions, they often ask you to calculate the field at a given distance or to describe the direction using the right‑hand rule.
| Scenario | Formula | Direction |
|---|---|---|
| Straight wire | \$B = \dfrac{\mu_0 I}{2\pi r}\$ | Use right‑hand rule (counter‑clockwise when looking along current) |
| Solenoid (inside) | \$B = \mu_0 n I\$ | Along the axis, from the end with the current entering to the end where it leaves |
| Solenoid (outside) | ≈ 0 (negligible) | Field lines almost cancel out |