Describe the pattern and direction of the magnetic field due to currents in straight wires and in solenoids

4.5.3 Magnetic Effect of a Current

Magnetic Field Around a Straight Wire

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.

Right‑Hand Rule for Direction

To find the direction of the magnetic field, use the Right‑Hand Rule:

  1. Point your thumb in the direction of the current (→).
  2. Wrap your fingers around the wire.
  3. Your fingers show the direction of the magnetic field lines (counter‑clockwise when viewed from the end of the wire).

🧲 Tip: Think of the wire as a magnet’s invisible hand, pulling the field lines around it.

Magnetic Field Inside a Solenoid

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.

Practical Example: The Electromagnet

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.

Exam Tips

  • Remember the formula for a straight wire: \$B = \dfrac{\mu_0 I}{2\pi r}\$.
  • Use the Right‑Hand Rule to determine direction; practice with different current directions.
  • For a solenoid, know that \$B = \mu_0 n I\$ and that the field is uniform inside.
  • Be able to sketch field lines: circles around a wire, straight lines inside a solenoid.
  • Check units: Tesla (T) = N/(A·m).

📝 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.

Quick Reference Table

ScenarioFormulaDirection
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