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A 100 eV proton is projected directly towards a large metal plate that has surface charge density of 2.2×10−6C/m2. From what distance (in mm) must the proton be projected, if it is to just fail to strike that plate?

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answer is 0.4.

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Detailed Solution

Applying conservation of mechanical energyΔK+ΔU=0 or Kf−Ki+Uf−Ui=00−100×1.6×10−19+1.6×10−19⋅ΔV=0ΔV=Ed=σε0d=2.2×10−68.8×10−12d0−100×1.6×10−19+1.6×10−19⋅2.2×10−68.8×10−12d=0d=100×8.8×10−122.2×10−6=4×10−4 m=0.4 mm

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