An electron in a vacuum chamber is fired with a speed of toward a large, uniformly charged plate away. The electron reaches a closest distance of before being repelled. What is the plate’s surface charge density?
The plate’s surface charge density is
The electron is fired with a speed of :
Distance from the uniformly charged plate :
The electron reaches a closest distance of :
Theory used :
The electric field owing to an infinite plane is calculated as follows:
The electron's force
The electron's work consists of the following:
Finally, we locate :
A parallel-plate capacitor has electrodes with surface charge densities . A proton traveling parallel to the electrodes at enters the center of the gap between them. By what distance has the proton been deflected sideways when it reaches the far edge of the capacitor? Assume the field is uniform inside the capacitor and zero outside the capacitor.
A small segment of wire in FIGURE contains of charge.
a. The segment is shrunk to one-third of its original length. What is the ratio of , where are the initial and final linear charge densities?
b. A proton is very far from the wire. What is the ratio Ff /Fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?
c. Suppose the original segment of wire is stretched to times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?
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