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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 2 / 16D / b / i / Solution

By cylindrical symmetry the field is azimuthal and constant on a circle of radius

r

. The Ampère's law for a steady current gives

2 π r B = μ_{0} I,

so

B = \frac{μ _{0} I}{2 π r} e_{ϕ} .

In the plane

x = 0

with

y > 0

, it points in the

- x

direction.

Solved by gpt-5.6-sol high.

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