At \(t=0\), electron 1 is shot out of an accelerator at a speed of \(2.0 \times 10^{3} \mathrm{~m} / \mathrm{s}\). At \(t=1.0 \mu \mathrm{s}\), electron 2 is shot out of the accelerator and travels on a path that is parallel to and \(10 \mathrm{~mm}\) below the path of electron 1 . The speed of electron 2 is \(5.0 \times 10^{3} \mathrm{~m} / \mathrm{s}\).

(a) At \(t=3.0 \mu \mathrm{s}\), what is the magnitude of the magnetic field at a point that is \(3.0 \mathrm{~mm}\) ahead of electron 1 and \(5.0 \mathrm{~mm}\) below it? Assume that the magnetic forces the electrons exert on each other for the \(2.0 \mu \mathrm{s}\) before you make your calculations do not alter the electrons' paths significantly.

(b) Show whether or not it is valid to assume that the magnetic forces the electrons exert on each other during the interval from \(t=1.0 \mu\) s to \(t=3.0 \mu\) s do not alter the electrons' paths significantly.