Two Parallel Conducting Plates with moving charge

[arl146]

Homework Statement

Two parallel conducting plates that are in deep space are brought to a potential difference of 3500 V, and a small pellet of mass 6.95 mg carrying a charge of 6.70 × 10-7 C accelerates from rest from the positive plate. With what speed will it reach the other plate?

Homework Equations

I'm thinking conservation of energy.
K_i+U_i=K_f+U_f

The Attempt at a Solution

I know that Ki ends up being 0 so it just becomes U_i=K_f+U_f. I have no idea what the potential energy would be since I don't have a distance.?

 

[anathema]

Hello! You are correct in thinking that conservation of energy will be useful in solving this problem. The potential energy in this case will be the potential difference between the two plates, which is given as 3500 V. The distance between the plates is not needed in this case since the electric potential energy only depends on the potential difference and the charge of the object.

So, using the conservation of energy equation, we can write:

(1/2)mv^2 + qV = 0 + 0

Solving for v, we get:

v = √(2qV/m)

Plugging in the values given in the problem, we get:

v = √(2(6.70 × 10^-7)(3500)/6.95 × 10^-6)

v = 4.14 × 10^3 m/s

Therefore, the pellet will reach the other plate with a speed of 4.14 × 10^3 m/s.

I hope this helps! Let me know if you have any further questions.