Consider a parallel plat capacitor with air between the two plates. The area of

Question

Consider a parallel plat capacitor with air between the two plates. The area of each plate is 0.5m2. The distance between the two plates is about 1mm. The capacitor is being charged with an 8V battery.

A particle of dust carries a charge of 1nC and a force of 8 x 10-6. If the dust particle (10-11kg) leaves from the negative plate with a speed of 35m/s, how far will the particle travel before it stops? Will the particle reach the positive plate?

Thank you for your help! (Please explain your answer so I understand it! :))

Explanation / Answer

Electric field between the parallel plates capacitor is

E = Q/eo A

as Q = CV

E = CV/eoA

but C = eoA/d

so

E = V/d

E = 8/1*10^-3

E = 8000 V/m

Now use Grav force = Electrical force

ma = E q

ma = E q

a = 8 *10^-6/(10^-11)

a = 8 *10^5 m/s^2

use the kinematic equation V^2 = 2 a S

S = 35^2/(2 * 8 *10^5)

S = 0.765 mm

No Plates does not reach + plate as distance is less than 1 mm

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