Problem 25.57 You sometimes create a spark when you touch a doorknob after shuff

Question

Problem 25.57 You sometimes create a spark when you touch a doorknob after shuffling your feet on a carpet. Why? The air always has a few free electrons that have been kicked out of atoms by cosmic rays. If an electric field is present, a free electron is accelerated until it collides with an air of 1 Figure 1 Atoms Electron knocked Electrons from first atom Original electron Breakdown of the air Hm Part A The average distance an electron travels between collisions is 2.0 um What acceleration must an electron have to gain 2.0x10 18 J of kinetic energy in this distance? Express your answer to two significant figures and include the appropriate units. a 1.1x 10 8 m. Submit My Answers Give Up Correct Part B What force must act on an electron to give it the acceleration found in part A? Express your answer to two significant figures and include the appropriate units F Value Units Submit My Answers Give Up

Explanation / Answer

Here ,

part A) let the acceleration is a

using work energy theorum

m * a * distance = kinetic energy

9.11 *10^-31 * a * 2 *10^-6 = 2 *10^-18

solving for a

a = 1.1 *10^18 m/s^2

part b)

let the force is F

F = m * a

F = 9.11 *10^-31 * 1.1 *10^18

F = 1 *10^-12 N

the force acting on the electron is 1 *10^-12 N

part c)

let the electric field is E

Force = q * E

1 *10^-12 = E * 1.602 *10^-19

E = 6.24 *10^6 N/C

the electric field is 6.24 *10^6 N/C

part d)

let the charge is q

E = k * q/d^2

6.24 *10^6 = 9*10^9 * q/(0.008)^2

solving for q

q = 4.44 *10^-8 C

the minimum charge is 4.44 *10^-8 C

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