Problem 2. A point-like particle with mass m and charge q moves in the (x, y)-plane...

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Problem 2. A point-like particle with mass m and charge q moves in the (x, y)-plane in the presence of uniform electric field E in the positive x-direction and uniform magnetic field B in the positive z-direction. Find the trajectory (x(t), y (t)) of the particle. Assume (for definiteness) that x(0) = y(0) = 0, v(0) = vo, and v(0) = 0, where Vo is the initial velocity (assumed to be known). Show that the particle drifts in the negative y-direction with the average drift velocity vd =-E/B. Problem 2. A point-like particle with mass m and charge q moves in the (x, y)-plane in the presence of uniform electric field E in the positive x-direction and uniform magnetic field B in the positive z-direction. Find the trajectory (x(t), y (t)) of the particle. Assume (for definiteness) that x(0) = y(0) = 0, v(0) = vo, and v(0) = 0, where Vo is the initial velocity (assumed to be known). Show that the particle drifts in the negative y-direction with the average drift velocity vd =-E/B.