An electron is released from rest at a distance of 0.350 m from a large insulati

Question

An electron is released from rest at a distance of 0.350 m from a large insulating sheet of charge that has uniform surface charge density 4.90×10^-12 C/m .

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 3.00×10^-2 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 3.00×10^-2m from the sheet?

 Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

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The sheet can be assumed to be infinite as it is given large .

Chrage density = = 4.90(10-12)C/m . The initial distance between sheet and electron is 0.350m.

Part A : The work done is given by W = (Force on electron) (distance moved by electron)

Electric filed of infinte thin sheet ,E = /2o = (4.90(10-12)C/m)/2(8.854(10-12)F/m) = 0.276V/m.

Force = QE = (1.6 (10-19)C)(0.276V/m) = 0.442(10-19) N.

Work done = (0.442N)((0.350 - 0.03)m)10-19 = (0.442)(0.32)(10-19)J = 0.141(10-19)J.

Part B : work done = kinetic energy of electron.

0.5mV2 = 0.141(10-19) . m = 9.11(10-31)kg gives V2 = 0.031(1012) (m/s)2= 3.1(1010) (m/s)2 Gives

V = 1.76(105) m/s

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