State the qualitative variation of the strength of the magnetic field around straight wires and solenoids

4.5.3 Magnetic Effect of a Current

Objective: State the qualitative variation of the strength of the magnetic field around straight wires and solenoids.

Magnetic Field Around a Straight Wire

Think of a straight wire as a spinning top that creates a swirling pattern of magnetic “air” around it. The closer you are to the wire, the stronger the swirl feels. This is described by the formula:

SymbolMeaning
\$B\$Magnetic field strength (T)
\$I\$Current through the wire (A)
\$r\$Distance from the wire (m)
\$\mu_0\$Permeability of free space (\$4\pi\times10^{-7}\,\text{T\,m/A}\$)

The relationship is:


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


So, as you move farther away (increase \$r\$), the field \$B\$ gets weaker – it drops off in proportion to \$1/r\$.

  • 🔌 Right‑hand rule: Point your thumb along the current direction; your fingers curl in the direction of \$B\$.

  • 📏 Inverse relationship: Double the distance → half the field strength.

  • ⚡ Current matters: More current → stronger field.

Exam Tip: When asked “How does \$B\$ change with distance?” remember the key phrase: “Inverse proportion to distance.” Write it as “\$B \propto 1/r\$” and give the full equation if required.

Magnetic Field Inside a Solenoid

A solenoid is like a coiled spring of wire. Inside this spring, the magnetic field lines are neat and straight, almost like a smooth river flowing from one end to the other. The field inside is much stronger than outside and is given by:

SymbolMeaning
\$B\$Magnetic field inside the solenoid (T)
\$\mu_0\$Permeability of free space
\$n\$Number of turns per unit length (\$N/L\$, turns/m)
\$I\$Current through the solenoid (A)

The formula is:


\$B = \mu_0 n I\$


Notice that \$B\$ is independent of distance from the centre (as long as you stay inside the solenoid) and depends directly on the current and the density of turns.

  1. 🔢 Count the turns: \$n = N/L\$.

  2. ⚡ Multiply: \$B = \mu_0 n I\$.

  3. 🧭 Direction: Use the right‑hand rule – thumb along the current, fingers show the field direction inside.

Exam Tip: When a question asks “What happens to \$B\$ if the number of turns is doubled?” answer: “\$B\$ doubles because \$n\$ doubles.” Also remember that \$B\$ inside a long solenoid is almost uniform; outside it is negligible.

Quick Comparison

FeatureStraight WireSolenoid
Field dependence on distance\$B \propto 1/r\$ (outside)Uniform inside; negligible outside
Key variables\$I\$, \$r\$\$I\$, \$n\$ (turns per length)
Direction ruleRight‑hand rule around wireRight‑hand rule along coil axis

Remember: The magnetic field is a vector – it has both magnitude and direction. Use the right‑hand rule to find the direction, and the formulas above to find how strong it is. Good luck with your studies! 🚀