ELECTROMAGNETISM & RELATIVITY - Chapter 4, Exercise 1 Solution
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Magnetic Field Around a Current-Carrying Wire

PROBLEM
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Calculate the magnetic field 0.1 m from a wire carrying a current of
15 A.

SOLUTION
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Using the compact working form of the magnetic field formula:

    B = (2 x 10^-7 x I) / r

Substitute the given values:

    I = 15 A
    r = 0.1 m

    B = (2 x 10^-7 x 15) / 0.1
    B = (3 x 10^-6) / 0.1
    B = 3 x 10^-5 T (30 uT)

ANSWER: The magnetic field 0.1 m from the wire is 3 x 10^-5 T, or
30 microtesla.

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WHY THIS WORKS AS AN ANSWER

The magnetic field around a straight current-carrying wire follows
the same inverse relationship with distance seen throughout this
course's own field formulas, though here it falls off as 1/r rather
than the 1/r^2 seen for electric and gravitational fields, since the
field spreads out around a line (the wire) rather than a point. Using
the compact working form (mu0/(2 pi) simplified to exactly 2 x 10^-7)
avoids needing to carry pi and mu0 through the calculation separately,
while giving the identical result. This 30 uT result is, as the
chapter notes, genuinely comparable in strength to Earth's own real
surface magnetic field (roughly 25-65 uT) - a real, everyday
demonstration of how significant a fairly modest current's own
magnetic effect actually is.