Think of an electric current as a stream of tiny charged “water” particles flowing through a wire. Just like a river creates swirling eddies around rocks, a current creates a magnetic field that circles the wire. The direction of the field depends on the direction of the current (right‑hand rule). The strength of the field is given by Ampère’s law:
\$B = \frac{\mu_0 I}{2\pi r}\$
Where \$I\$ is the current, \$r\$ is the distance from the wire, and \$\mu_0\$ is the magnetic constant.
Exam Tip: When asked to sketch the field around a straight wire, remember the right‑hand rule: point your thumb along the current direction, and your fingers curl in the direction of the magnetic field.
A solenoid is a coil of wire that behaves like a long bar magnet when current flows through it. Inside the coil, the magnetic field lines are almost straight and parallel, giving a strong, uniform field. Outside, the field is weak and spreads out like a gentle breeze.
The magnetic field inside a long solenoid is:
\$B = \mu_0 n I\$
Where \$n\$ is the number of turns per unit length and \$I\$ is the current.
| Parameter | Effect on B |
|---|---|
| Current \$I\$ | Directly proportional (↑I → ↑B) |
| Turn density \$n\$ | Directly proportional (↑n → ↑B) |
| Direction of I | Reverses field direction (north ↔ south) |
Exam Tip: For a solenoid, remember that the field inside is uniform and given by \$B = \mu_0 n I\$. If the question asks about the field outside, note that it is much weaker and can be approximated as zero for a long solenoid.
Wrap a coil of wire around a nail (the core). When you connect a battery, the current creates a magnetic field that turns the nail into a magnet. Increase the battery voltage or add more turns, and the nail becomes a stronger magnet. Flip the battery leads, and the magnet’s north and south poles swap places. This is a classic demonstration of how changing the magnitude and direction of current controls magnetic fields.
Quick Check: If you double the current in a straight wire, by what factor does the magnetic field at a fixed distance change? (Answer: It doubles.)