In the following velocity selector, the positive plate of the capacitor is above

Question

In the following velocity selector, the positive plate of the capacitor is above the negative as shown. The voltage of the battery is 19 voilts and the distance between the plates is 17 mili-meter Ino diclectric). A uniform magnetic field of 90 mill-Tesla is in the -z direction. A point charge of-18 micro-coulombs with a mass of 9 gras is passing through at 25 percent of the speed not to be deflected. It is initially moving horizontally in the +x direction If the length of the plates is 3 meters, how far will the charge be deflected (vertically) in micro-meters (1 x 10 m) by the time it exits the velocity selector? lenore the weight Uniform magnetic field in the -i direction (into the plane)

Explanation / Answer

given
V = 19 V
d = 17*10^-3 m
hence
E = V/d = 1117.647 V/m

B = 90*10^-3 T
q = -18*10^-6 C
m = 9*10^-3 kg
v = 0.25vo
l = 3 m

now,
from force balance
qvo*B = qE
vo = E/B

now, acceleration = a
a = F/m
F = qE - qvB = q(E - 0.25E) = 0.75qE
a = 0.75qE/m = 1.6764 m/s/s

now, time taken to complete the journey = t
0.25E*t/B = l
t = 4Bl/E

hence
deflection = y
y = 0.5*a*t^2 = 8.748*10^-4 m = 874.8*10^-6 m

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