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Field on axis of a coil
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Field falls off along the axis.
B = μ₀IR²/(2(R² + x²)^{3/2}) on the axis, maximal at the centre and falling as 1/x³ far away.
At x = R it's 35% of the centre value.
Used for Helmholtz coils.
In more detail
On the axis of a coil, the field at distance z from its centre is B = μ0NIR²/(2(R²+z²)^(3/2)). It falls off with distance from the coil.
Real-world uses
- Helmholtz coils and magnetic sensors are designed using axial fields.
- MRI coils use axial field patterns.
- Hall probes and magnetic sensors are positioned along the axis of a coil to measure the field strength.
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Frequently asked questions
Is the field uniform along the axis?
Only near the centre, where it is nearly constant over a region.
Why does it fall off with z?
Because the coil's field spreads out and points more obliquely away from the centre.
Why does the field fall off along the axis?
Points further from the coil are more remote from its current, so the field decreases as the distance increases.
Related topics in Magnetism & Induction
Biot–Savart law · Field of a long straight wire · Field at centre of a loop · Field of a solenoid · Toroid · Ampere's law