(i) A charged particle at rest or moving experiences a force ®F= q®E in the presence of electric field. The acceleration, velocity and displacement are given by
(ii) For a charged particle with initial velocity perpendicular to the electric field Note that Fx = 0, ax = 0, Vx = u at all times
Fy = qE, ay = (qE/m), Vy = (qE/m)t
The displacement components are x = ut
y = (1/2)(qE/m)t2
Eliminating t, y = (1/2) (qE/mu2)X2 which is the equation of a parabola.
(iii) The path of a charged particle entering a region of electric field with initial velocity perpendicular
to the field follows a parabolic trajectory.
The time spent in electric field is t = (L/u) (sec fig.A) The y component of velocity when it emerges
out of the field region is Vy = (qEL/mu)
The resultant velocity
The angle at which the particle emerges
tanq = (Vy/Vx) = (qEL/mu2)
The height Y at which the particle hits the screen (see fig. A)
Y = D tanq
Y = (qELD/mu2)
Y = (qELD/2K) (where K is initial kinetic energy)
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