Two stationary positive point charges, charge 1 of magnitude 3.65 nC and charge

Question

Two stationary positive point charges, charge 1 of magnitude 3.65 nC and charge 2 of magnitude 1.60 nC , are separated by a distance of 38.0 cm. An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.

What is the speed vfinal of the electron when it is 10.0 cm from charge 1?

Two stationary positive point charges, charge 1 of magnitude 3.65 nC and charge 2 of magnitude 1.60 nC , are separated by a distance of 38.0 cm. An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.

What is the speed vfinal of the electron when it is 10.0 cm from charge 1?

Explanation / Answer

note: the net force acting on the electron due to 2 charges is NOT a constant, we can't use F = ma the find its speed. Use energy relation instead since the total energy (kinetic + electric potential) is conserved.
use Q1 = 3.65 nC, Q2 = 1.6 nC, 2d = 38.0 cm, a = 10.0 cm, q = -1.6 x 10^(-19) C (electron charge)
initial kinetic energy = 0
initial electric potential energy = KqQ1/d + KqQ2/d = Kq(Q1 + Q2)/d
final kinetic energy = mv²/2
final electric potential energy = KqQ1/a + KqQ2/(2d - a) = Kq*[Q1/a + Q2/(2d - a)]
energy conservation:
0 + Kq(Q1 + Q2)/d = mv²/2 + Kq*[Q1/a + Q2/(2d - a)]
plug all the know values and K = 9.0 x 10^9 to find v(m=9.11e-31)

3.98x10^-19=9.11e-31*v²/2+

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