Field at centre of a loop

Intermediate

Field at the centre of a circular coil.

Key relationB = μ₀I/2R

B = μ₀NI/(2R) for N turns of radius R, pointing along the axis.

Worked example

N = 50, I = 2 A, R = 10 cm: 0.63 mT.

Common mistake

Right-hand rule gives the direction.

In more detail

At the centre of a circular loop of radius R carrying current I, the field is B = μ0I/(2R). It points perpendicular to the plane of the loop.

Designing coils that produce a uniform field near their centre.
Measuring magnetic fields in lab experiments with loops.
A coil of wire wound into a loop produces a strong, uniform field at its centre, which is used in instruments.

Which direction is the field?

Use the right-hand rule: curl fingers in the current direction, and the thumb gives the field.

How can I increase the field?

Use more turns or a larger current, or reduce the radius.

Does adding more turns increase the field?

Yes. The field at the centre grows in proportion to the number of turns, for the same current.