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Answer #1

The electric potential is not necessary to solve this problem.
Let k (Coulomb's constant) = 9*10^9
r = 2.4 [m]
d = 5 [m]
e (charge on electron) = -1.6*10^-19
m of electron = 9.1*10^-31 [kg]
Conserving the energy of the system ->
E_initial = E_final
U_electrical_i + K_mechanical_i = U_electrical_f + K_mechanical_f
At infinity, electric potential energy is 0, at final position, velocity is 0 (therefore K = 0)
At final position, there is electric potential energy due to the ring and due to the point charge; the potential due to the ring is positive and the potential due to the charge is negative because an electron is negatively charged.
The distance from the ring to the electron is equal at points and is given by ?d^2 + r^2
This gives
0.5*m*u^2 = | ( k*e*Q / ?d^2+r^2 ) - ( k*q*e / d^2 ) |
Solving for u
u = 6.649 [Mm/s] or 6.649*10^6 [m/s] <-------- ANS

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