A particle with mass m and charge q is emitted from the origin, (x, y) = (0, 0).

Question

A particle with mass m and charge q is emitted from the origin, (x, y) = (0, 0). A large, flat fluorescent screen is located at x = L. There is target on the screen at y position y_2 > 0. Igno5re gravity in this problem. Suppose the charge is emitted with velocity v_0 in the positive x-direction. Between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. What should the magnitude E of the electric field be if the charge is to hit the largest on the screen? Express your answer in terms of m, q, y_2, v_0, and L. When entering the answer, note the warnings about proper format.

Explanation / Answer

Here, time taken , t = L/vo

Also, yh = 1/2 * a * t2

where, qE = ma

=>   yh = 1/2 * (qE/m) * (L/vo)2

=>    E = 2yh * (vo/L)2 * (m/q)

Thus, magnitude of electric field , E = 2yh * (vo/L)2 * (m/q)

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