3. 0/1 points| Previous Answers My Notes An electron starts from rest 5.00 cm fr

Question

3. 0/1 points| Previous Answers My Notes An electron starts from rest 5.00 cm from the center of a uniformly charged insulating sphere of radius 4.00 cm and total charge 1.44 nC. What is the speed of the electron when it reaches the surface of the sphere? (Note: Assume a reference level of potential V-0 at r = “.) 1.296e10 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s Submit Answer Save Progress Practice Another Version

Explanation / Answer

the initial speed

Vi = 0

r1 = 5 cm

= 0.05 m

r2 = 4 cm

= 0.04 m

q = 1.44 nC

= 1.44 X 10-9 C

k = 9 X 109 Nm2/C2  

using equations of PE and KE

1/2 m vf2 - 1/2 mvi2 + e k q ( 1/r1 - 1/ r2 ) = 0

1/2 m vf2 = 1/2 mvi2 - e k q ( 1/r1 - 1/ r2 )

1/2 m vf2 = 1/2 mvi2 + e k q ( 1/r2 - 1/ r1 )

vf2 = ( 2/m ) X (1/2 mvi2 + e k q ( 1/r2 - 1/ r1 ) )

vf2 = ( 2/m ) X (1/2 m X 02 + e k q ( 1/r2 - 1/ r1 ) )

vf2 = ( 2/m ) X ( e k q ( 1/r2 - 1/ r1 ) )

vf2 = ( 2/m ) X ( e k q ( 1/r2 - 1/ r1 ) )

Vf = [ ( 2 e k q / m ) ( 1/r2 - 1/ r1 ) ]1/2

Vf = [ ( 2 X 1.6 X 10-19 X 9 X 109 X 1.44 X 10-9 / 9.1 X 10-31 ) ( 1/0.04 - 1/ 0.05 ) ]1/2   

Vf = 4.773553518 X 106 m/s

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