Consider the motion of a charged particle of mass m and charge q in an electric
ID: 3113278 • Letter: C
Question
Consider the motion of a charged particle of mass m and charge q in an electric field.
Consider the motion of a charged particle of mass m and charge q in an electric field (for example, in a cathode ray tube or a CRT monitor). In the absence of a magnetic field and gravity, the force exerted on the particle due to a constant electric field with strength E is given by F = qE Suppose there are two plates of length l that create a constant electric field E_0 pointing in the negative y direction, that is E= E_0y See the figure below. Furthermore, suppose that when the particle enters the plate region, it is moving in the positive x direction at a constant velocity v_0. (a) Find the position functions x(t) and y(t), assuming that the plate region starts at (x, y) = (0, 0). (b) Suppose that when the particle leaves the region, it has been vertically displaced by an amount Delta_y. What is the charge q? Assume that the plates are far enough apart so that the particle actually leaves the region. (c) Compute y(t) when we account for gravitational forces.Explanation / Answer
(a) Initially, velocity in x direction and y direction are
V0x = v0=constant, V0y = 0
After time t, velocity in Y direction becomes, Vy =1/2 ayt ( from v = u+at)
Where ay = - E0q/m, since force on particle = -E0q
Thus, x(t) = v0t and y(t) = 1/2 ayt2 = 1/2(-qE0/m)(x/v0)2
As, t = x/v0, thus, y(t) = 1/2(-qE0/m)(x2/v02)
(b) Putting y(t) = y and x =l in equation of y(t) we get
y =1/2(-qE0/m)(l2/v02),
Hence, q = -(2ymv02/E0l2)