# Maximum initial speed the electron can have without hitting the negative plate

Two parallel plates are 2.0 cm apart and the electric ﬁeld strength between
them is 1.0 × 10^4 N/C. An electron is launched at a 45 degree angle from the
positive plate. What is the maximum initial speed v0 the electron can have
without hitting the negative plate?

i think the answer is 1.3x10^7 m/s. can someone confirm this?

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berkeman
Mentor
Two parallel plates are 2.0 cm apart and the electric ﬁeld strength between
them is 1.0 × 10^4 N/C. An electron is launched at a 45 degree angle from the
positive plate. What is the maximum initial speed v0 the electron can have
without hitting the negative plate?

i think the answer is 1.3x10^7 m/s. can someone confirm this?
It would be much easier for us to confirm it if you posted your work for us to see. Remember, that's part of the PF rules -- posting your attempt at the solution.

The acceleration = F/m = E*q/m

So at y max vy = 0 so

vy^2 = vy0^2 - 2*E*q/m*ymax

So vy0 = sqrt(2*E*q/m*ymax) = sqrt(2*1.20x10^4*1.60x10^-19/9.11x10^-31… = 9.18x10^6m/s

So v0 = vy0/sin(45) = 9.18x10^6m/s/sin(45) = 1.30x10^7m/s