[tex]\text{An infinite plane charge with }\sigma=\text{65.0 nC/m}^2\text{ lies}\\\text{in the }xy\text{ plane. Recall that the electric field due}\\\text{to a non-conducting plane of charge in the }xy\text{ plane}\\\text{may be expressed as }\vec{E}=\dfrac{\sigma}{2\epsilon_0}\dfrac{z}{|z|}\hat{k}.\\(a)\;&\text{Using the given equation of the electric field,}\\\text{}\hspace{17pt}\text{determine the general expression for the}\\\text{}\hspace{17pt}\text{potential difference between two values of }z,\\\text{}\hspace{17pt}\text{where }z\ \textgreater \ 0.\text{ Express your answer in terms of}\\\text{}\hspace{17pt}\text{initial and final points }z_i\text{ and }z_f.\\(b) \text{ Using your answer from part }a,\text{ determine the}\\\text{}\hspace{17pt}\text{potential difference between }z_i=5.80\text{ m and }\\\text{}\hspace{17pt}z_f=0.35\text{ m.}\\(c)\text{ A proton is moving towards the plane. If its}\\\text{}\hspace{17pt}\text{initial velocity is }\vec{v}=-3.05\times 10^6\;\hat{k}\text{ m/s at }\\\text{}\hspace{17pt}z=5.80\text{ m, what will its velocity be at}\\\text{}\hspace{17pt}z=0.35\text{ m? You may assume that the proton}\\\text{}\hspace{17pt}\text{does not come to a stop before reaching the }\\\text{}\hspace{17pt}\text{plane.}[/tex]

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