Suppose electrons move through a copper wire at speed \(v\). Call the linear charge densities in the Earth reference frame \(\lambda_{E_{p}}\) for the fixed positive ions in the wire and \(\lambda_{\mathrm{Fn}}\) for the (negative) electrons. Observer E in the Earth reference frame (which is also the reference frame of the positive ions) measures the wire to be electrically neutral. Observer \(\mathrm{M}\) is moving along with the electrons (in the same direction as the electrons and at speed \(v\) ). Calculate the linear charge density of the wire as measured by \(\mathrm{M}\) in terms of \(\lambda_{\mathrm{Fn}}\) if the speed is

(a) \(3.0 \times 10^{5} \mathrm{~m} / \mathrm{s}\) and

(b) \(3.0 \mathrm{~mm} / \mathrm{s}\) (an achievable speed for electrons in copper wire).