A positive small charged particle q = 1 mu C and mass of m = 2 x 10^-12 kg is pu

Question

A positive small charged particle q = 1 mu C and mass of m = 2 x 10^-12 kg is put into a uniform electric field vector E = 4 x 10^6 (N/C) region which direct to the positive is x direction. The particle at rest travels hum the position A: (xA = 0, yA = 0) to the position B: (xB = 0.01m, yB = 0). Here samll charged particles means its presence does not change the electric field. The following questions may not be dependent; if you cannot do some move to the next. Determine the force and acceleration of the particle. Calculate the work done by the electric force to the particle from A to B. Determine the final speed of the particle

Explanation / Answer

Given:-

q= 1uC

m=2*10-12 kg

E= 4*10 6 N/C

A= [0,0]m to B= [ 0.01,0]m

a]

F= qE

F= ma

qE= ma  

a= qE/m=1*10 -6*4*10 6 / 2*10-12 = 2*1012m/s2

F= ma= 4N

b]

work done = q[VB- VA ] [ V= w/q ]

V= Ed = 4*10 6 *0.01=4*104v

w = qV =1*10 -6*4*10 4 = 0.04 J

c]

work done = KE

0.04 J= 1/2mv2

2*0.04/2*10-12 =v2

v= 2*105 m/s------------- speed of the particle

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