An electron is released from rest at a distance of 0.580 m from a large insulati

Question

An electron is released from rest at a distance of 0.580 m from a large insulating sheet of charge that has uniform surface charge density 4.70×1012 C/m2 .

A) How much work is done on the electron by the electric field of the sheet as the electron moves from its initial position to a point 7.00×102 m from the sheet? Express your answer to three significant figures and include the appropriate units.

B) What is the speed of the electron when it is 7.00×102 m from the sheet? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

A)we know that,

E = sigma/2 epsilon0

E = 4.7 x 10^-12/(2 x 8.85 x 10^-12) = 0.266 N/C

force experienced due to electric field will be:

F = qE

F = qE  = 1.6 x 10^-19 x 0.266 = 4.256 x 10^-20 N

from the defination of work done:

W = Fd

W = 4.256 x 10^-20 N x 7 x 10^-2 = 2.979 x 10^-21 J

Hence, W =  2.979 x 10^-21 J

B)from conservation of energy:

W = 1/2 m v^2

v = sqrt (2W/m) = sqrt (2 x  2.979 x 10^-21 / 9.1 x 10^-31) = 8.092 x 10^4 m/s

Hence, v = 8.092 x 10^4 m/s

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