Two point charges are fixed 4.0 cm apart from each other. Their charges are Q_1

Question

Two point charges are fixed 4.0 cm apart from each other. Their charges are Q_1 = Q_2 = 5.5 muC, and their masses are m_1 = 1.5 mg and m_2 = 3.5 mg. If Q_1 is released from rest, what will be its speed after a very long time? Express your answer to two significant figures and include the appropriate units. Part B If both charges are released from rest at the same time, what will be the speed of Q_1 after a very long time? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Part A

When no outside forces such as friction acts on an system, the total energy of the system is constant. That is, the sum of kinetic, and potential energies at one point is the same as at any other time.
Etotal = (0.5)mv2 + U is unchanging if no work is done on the system.

Since they carry equal charge they will repel when released and move to an infinite distance after a long time. At that point potential energy will be zero.

U = 0.5mv2

kq2/d = 0.5mv2

9*109*(5.5*10-6)2/0.04 = 0.5*3.5*10-3v2

v = 62.36 m/s

B) Now both particles will move apart

The total energy is
Etotal = 2(0.5)mv2 + kQq/r

kq2/d = 2*0.5mv2

9*109*(5.5*10-6)2/0.04 = 2*0.5*3.5*10-3v2

v = 44.1 m/s

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