An infinite non-conducting plane of positive charge density sigma is orientated

Question

An infinite non-conducting plane of positive charge density sigma is orientated as shown in the diagram. The plane has infintestimal thickness. the plane is at x=0. Also a point charge +q is located at x=d. This charge is held in place here at this position permenantly. The points x=a and x=b are reference points for the problem. An electron of mass m and charge -e is shot out of a gun at x=a in the direction of x=b. The initial speed of the electron is V0. Answer the following in terms of quantities given or a subset of thereof.

a) Use Gauss' law to show the electrif field due to the infinite plane is sigma/2e0

b)What is the total electrif fild on the x-axis for x>d

c) Just as the electron leaves the gun what is the force on the electron

d) What is the speed of the electron at x=b

e) Will the electron ever have a zero speed, if so what is the euqation that will enable you to solve for the position of the electron when its speed is zero?

Explanation / Answer

a)let us consider a cylinder passing through the surfaces of the plance.so by gauss's law,

E.dA=q/eo

or E*2A=q/eo (2A since two surfaces of the cylinder)

or E=sigma/(2eo)

b)total electric field=(sigma/2eo)+ kq/(x-d)^2

c)conserving energy,

-e*(sigma/2eo)*(a-b) + -( kqe/b - kqe/a) +0.5mv^2 =0.5mvo^2

or mv^2=mvo^2 + e*(sigma/2eo)*(a-b) + kqe/b - kqe/a

d)yes, the energy conservation by a similar method will give us our result

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