A small object with mass m, charge q, and initial speed Vo = 5.00×103 m/s is pro

Question

A small object with mass m, charge q, and initial speed Vo = 5.00×103 m/s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm Figure 1). The electric field between the plates is directed downward and has magnitude E 800 N/C Assume that the field is zero outside the region between the plates. The separation between the plates is large enough for the object to pass between the plates without hitting the lower plate. After passing through the field region, the object is deflected downward a vertical distance d = 1.45 cm from its original direction of motion and reaches a collecting plate that is 56.0 cm from the edge of the parallel plates. Ignore gravity and air resistance Figure 1 of 1 56.0 cm DO

Explanation / Answer

time to pass between the plates

t = d / v

t = 0.26m / 5000 m/s

t = 5.2 x 10^-5 s

time to travel the additional 56 cm:

t' = 0.56m / 5000 m/s

t' = 1.12 x 10-4 s

the vertical velocity at the edge of the plates is

v = a*t

where a = field-induced acceleration between the plates

s = v*t' + 1/2at^2

s = a*t*t' + 1/2at^2

s = a*(t*t' + 1/2t^2)

0.0145 m = a* [(5.2 x 10^-5 x 1.12 x 10^-4 + 0.5*(5.2 x -5)^2)

0.0145 = a[ (5.84 x 10^-9) + (1.312 x 10^-9)

a = 2.02 x 10^6 m/s^2

F = m*a = q*E

q/m = a / E

q/m = (2.02 x 10^6 m/s^2 / 800 N/C

q/m = 2525 C/kg

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