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Two identical +9.5 microcoulomb point charges are initially 5.3 cm from each oth

ID: 1583992 • Letter: T

Question

Two identical +9.5 microcoulomb point charges are initially 5.3 cm from each other. If they are released at the same instant from rest, how fast will each be moving when they are very far away from each other? Assume they have identical masses of 1.00 mg. [Start by finding the electric potential, in volts, at 3.50cm from ONE of these charges. THEN calculate the EPE of the SECOND charge when it is placed at the point (EPE = qV). NOW do a straight energy conservation problem. The two charges start with that EPE and zero KE. Then assuming they have equal KE moving in opposite directions, find the speeds of each of them. One possible point of confusion is whether EACH charge has the EPE, or whether there is only ONE EPE that they share. The answer is the latter. Unlike forces (where there is always an opposite pair), the EPE is the energy it takes to bring the charges TOGETHER, and it does not matter which one was there first. ONE value for the pair.]

Explanation / Answer

given

Q = 9.5 micro C

d1 = 5.3 cm = 0.053 m

d2 = infinite

m = 1 mg = 1*10^-6 kg

let v is the speed of the charged particles when they move infinite distance.

Apply conservation of energy

U1 + KE1 = U2 + KE2

k*Q^2/d1 + 0 = 0 + 2*(1/2)*m*v^2

k*Q^2/d1 = m*v^2

v^2 = k*Q^2/(m*d1)

v = sqrt(k*Q^2/(m*d1))

= sqrt(9*10^9*(9.5*10^-6)^2/(1*10^-6*0.053))

= 3915 m/s <<<<<<<----------------------------Answer

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