On average, the number density of free electrons in copper is \(8.46 \times 10^{19} \mathrm{~mm}^{-3}\).

(a) Calculate what the linear charge density \(\lambda\) for a copper wire \(1.00 \mathrm{~mm}\) in radius would be if this quantity of electrons were missing.

(b) Assume this copper wire is electrically neutral in the Earth reference frame, in which it is at rest and carrying a current. Calculate the linear charge density \(\lambda^{\prime}\) of the copper wire in a reference frame moving along with the electrons if the electrons are moving at \(4.70 \times 10^{-4} \mathrm{~m} / \mathrm{s}\).