A potassium ion with an initial velocity of 106 m/s i-hat is shot through the ce

ID: 2271280 • Letter: A

Question

A potassium ion with an initial velocity of 106 m/s i-hat is shot through the center of two capacitor plates

located at y = 8 cm and y = ?8cm. The plate at y = 8 cm has a charge of ?10 nC and the plate at y = ?8 cm

has a charge of +10 nC. The plates are circular with a radius of 3 cm.

a) Neglecting gravity, what is the y position of the ion as it exits the capacitor?

b) Now including gravity which pulls the ion towards the positively charged plate, what is the y

position of the ion as it exits the capacitor?

Electric field between plates,

E = sigma/epsilon

epsilon = 8.85418782 * 10^(-12)

sigma = charge / area

charge = 10^(-8)

area = pi* r^2

r = 0.03

so, E = 399636 N/C

distance covered by charge, d = 2*r

q = 1.6* 10^(-19)

m = 19*1.66 * 10*(-24)

v = 0 (along y-direction)

a) a = F/m

F = q*E

so, a = -8.477 * 10^(-18) m/s^2

time taken to travel the distance in electric field, t = d/106 = 0.000566 seconds

let y-position be s

s = 0.5*a*t*t

s = -1.353 * 10^(-24) m

b) with gravity,

a = -10

so,

s = -1.602 * 10^(-6) m

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