Answer
(a) $B = 2.0\times 10^{-6}~T$
(b) 4.0%
Work Step by Step
(a) We can find the magnetic field at the point:
$B = \frac{\mu_0~I}{2~\pi~r}$
$B = \frac{(4\pi\times 10^{-7}~T~m/A)~(200~A)}{(2~\pi)~(20~m)}$
$B = 2.0\times 10^{-6}~T$
(b) We can express this value as a percentage of the Earth's magnetic field:
$\frac{2.0\times 10^{-6}~T}{50\times 10^{-6}~T}\times 100\% = 4.0\%$
