[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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Question video: determining the plane in which a given point lies. Point if between lies points ex two euclid class deleted geometry introduction chapter next. Lines points plane line postulate intersect intersection two if point geometry planes distinct basic also ck
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