An electron is released from rest at the negative plate of an air filled paralle

Question

An electron is released from rest at the negative plate of an air filled parallel plate capacitor. The charge per unit area on each plate is 1.80 x 10 C/m , and the plate separation is 1.50 cm. How fast is the electron moving just before it reaches the 7 2 positive plate? Note that, for an air illd parallel plate capacitor, the magnitude of the electric field between the plates is: where is the charge per unit area, q is the magnitude of the charge on the plates, A is the area of one plate. Select one: a. 4.88 x 10 J b. none of the above c. 1.03 x 10 m/s d. 1.03 x 10 m/s e. 2.03 x 10 m/s 7 8 4

Explanation / Answer

here,

the charge per unit area , sigma = 1.8 * 10^-7 C/m^2

electric feild , E = sigma /e0

E = 1.8 *10^-7 /( 8.85 * 10^-12) = 2.03 * 10^4 N/C

d = 1.5 cm = 0.015 m

let the speed of electron be v

work done by potential = kinetic energy gained

(E * d) * q = 0.5 * m * v^2

2.03 * 10^4 * 0.015 * 1.6 * 10^-19 = 0.5 * 9.1 * 10^-31 * v^2

solving for v

v = 1.03 * 10^7 m/s

the speed of electron is c) 1.03 * 10^7 m/s

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