Walker, Halliday & Resnick — Magnetic Fields: Problem 37

37 An electron moves through a uniform magnetic field given by \(\vec{B} = B_x\hat{i} + (-3.0B_x)\hat{j}\). At a particular instant, the electron has velocity \(\vec{v} = (2.0\hat{i} + 4.0\hat{j})\text{ m/s}\) and the magnetic force acting on it is \((6.4 \times 10^{-19}\text{ N})\hat{k}\). Find \(B_x\).