Magnetic Fields in Solenoids
Ampere's Law relates the integrated magnetic field around a closed loop to the electric current passing through that loop. While it is a complex calculus-based law, its most practical application is calculating the magnetic field inside a solenoid (a coil of wire).
A solenoid is the basis for electromagnets, inductors, and even the valves in your car's fuel injectors. Inside an ideal solenoid, the magnetic field is remarkably uniform and strong, while outside, it is nearly zero.
Factors Affecting Solenoid Strength
- Turn Density ($n$): The number of turns per meter of length ($N/L$). More tightly packed coils produce stronger fields.
- Current ($I$): Increasing the current linearly increases the magnetic field strength.
- Core Material: While this formula assumes an air core, adding a "ferromagnetic" core (like iron) can increase the field strength by thousands of times.
The Formula
Where:
B=
Magnetic Field (Tesla, T)=
Permeability (4π × 10⁻⁷ T·m/A)N=
Total number of turnsL=
Length of solenoid (meters)I=
Current (Amperes)Example Calculation
You have a solenoid $0.2 , \text{m}$ ($20 , \text{cm}$) long with $500$ turns of wire. You pass $2 , \text{Amps}$ through it.
- Calculate n ($N/L$): $500 / 0.2 = 2,500 , \text{turns/meter}$.
- Multiply by Constant and Current: $(4\pi \times 10^{-7}) \times 2,500 \times 2 \approx 0.00628 , \text{T}$.
The field inside is roughly $6.3 , \text{mT}$.