(a) Does the proton reach the plate? (b) If not, how far from the plate does it turn around?

Question

From a distance of 10 cm, a proton is projected with a speed of 𝑣=4.0×106m/s directly at a large, positively charged plate whose charge density is 𝜎=2.0×10−5C/m2. (a) Does the proton reach the plate? (b) If not, how far from the plate does it turn around?

Answer 1

Compare the kinetic energy at 10 cm to the work that could be done by the plate if the particle could move 10 cm toward the plate.

pThat work would be negative. If the magnitude of the work computed is less than the kinetic energy at 10 cm, it will reach the plate.

Answer 2

You are looking for the distance that the proton will go for a given kinetic energy against a constant E field

The electrical potential energy is q_pV = q_pEd = q_pd(σ/2ε₀) (E = σ/2ε₀) for an infinite plate

The kinetic energy is (1/2)m_pv²

Equating the two and solving for d: d = ε₀m_pv²/(q_pσ)

a) Compare d with 10 cm b) If d is less than closest distance to the plate is 10 - d

Remember to convert d to cm for comparison.

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