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

Published by Patrick Mutisya · 14 days ago

Magnetic Effect of a Current – IGCSE Physics 0625

4.5.3 Magnetic Effect of a Current

Objective

Describe the pattern and direction of the magnetic field produced by:

  • Currents in straight wires

  • Currents in solenoids

1. Magnetic Field Around a Straight Current‑Carrying Conductor

When an electric current flows through a straight wire, a magnetic field is generated in the space surrounding the wire. The field lines are concentric circles centred on the wire.

1.1 Direction – Right‑Hand Thumb Rule

To determine the direction of the magnetic field:

  1. Grip the wire with the right hand so that the thumb points in the direction of conventional current (positive to negative).

  2. The curled fingers show the direction of the magnetic field lines around the wire.

Suggested diagram: Straight wire with current upward, magnetic field lines forming concentric circles, right‑hand thumb rule illustration.

1.2 Field Strength

The magnitude of the magnetic field at a distance \$r\$ from a long straight conductor carrying current \$I\$ is given by Ampère’s law:

\$B = \frac{\mu_0 I}{2\pi r}\$

where \$\mu_0 = 4\pi \times 10^{-7}\ \text{T·m·A}^{-1}\$ is the permeability of free space.

2. Magnetic Field Inside a Solenoid

A solenoid is a coil of many turns of wire. When a current flows through the coil, the magnetic field inside the coil is strong and nearly uniform, while the field outside is weak.

2.1 Direction – Right‑Hand Grip Rule for Solenoids

  1. Wrap the fingers of the right hand around the solenoid in the direction of the current flowing through the coils.

  2. The extended thumb points in the direction of the magnetic field inside the solenoid (from the South to the North pole).

Suggested diagram: Solenoid with current direction shown, magnetic field lines inside (parallel) and outside (sparse), right‑hand grip rule illustration.

2.2 Field Strength Inside a Long Solenoid

For a solenoid of \$n\$ turns per unit length carrying a current \$I\$, the magnetic field inside is:

\$B = \mu_0 n I\$

This expression assumes the solenoid is sufficiently long that edge effects are negligible.

2.3 Comparison of Straight Wire and Solenoid Fields

FeatureStraight WireSolenoid
Field patternConcentric circles around the wireParallel, uniform lines inside; weak, divergent lines outside
Direction ruleRight‑hand thumb ruleRight‑hand grip rule
Field magnitude formula\$B = \dfrac{\mu_0 I}{2\pi r}\$\$B = \mu_0 n I\$ (inside, long solenoid)
Dependence on distanceDecreases with \$1/r\$Approximately constant inside; negligible outside

3. Key Points to Remember

  • The magnetic field produced by a current is always perpendicular to the direction of the current.

  • Use the right‑hand thumb rule for a single straight conductor and the right‑hand grip rule for a solenoid.

  • In a long solenoid the field inside is strong and uniform, making solenoids useful as electromagnets.

  • The field strength around a straight wire falls off with distance, whereas the field inside a solenoid is essentially independent of position (away from the ends).

4. Sample Questions

  1. A straight wire carries a current of \$5\ \text{A}\$. Calculate the magnetic field \$5\ \text{cm}\$ from the wire.

  2. A solenoid has 800 turns and a length of \$0.40\ \text{m}\$. If a current of \$2\ \text{A}\$ flows through it, find the magnetic field inside the solenoid.

  3. Explain how you would use the right‑hand rule to determine the direction of the magnetic field at a point located to the right of a vertical current‑carrying wire.