Two particles,each having a mass of 3.0$\mu$g and having equal but opposite charges of magnitude of 6.0 nC,are released simultaneously from rest when they are a very large distance apart.What distance separates the two at the instant when each has a speed of 5.0 m/s?
A)4.3 mm
B)8.6 mm
C)7.3 mm
D)5.6 mm
E)2.2 mm

Question

Quizplus · Accepted Answer

The distance between the particles can be calculated using the conservation of energy principle. At any point, the potential energy between the particles is given by:
U = (k*q^2)/r, where k is the Coulomb constant (=9x10^9 Nm^2/C^2), q is the magnitude of charge (6.0 nC = 6x10^-9 C), and r is the distance between the particles.
At the initial position, the potential energy is zero (since they are infinitely far apart), and at the final position (where they have a speed of 5.0 m/s), the potential energy is -(k*q^2)/(2r), as they have equal but opposite charges and the potential energy is negative.
The kinetic energy of each particle at that point is (1/2)*m*v^2, where m is the mass (3.0x10^-10 kg), and v is the speed (5.0 m/s).
By the conservation of energy principle, the initial total energy (zero) is equal to the final total energy (kinetic energy + potential energy). Hence we have:
0 = 2*(1/2)*m*v^2 - (k*q^2)/(2r)
Solving for r gives: r = (k*q^2)/(2*m*v^2) = 4.3 mm

Therefore, the answer is A) 4.3 mm.

Two Particles,each Having a Mass of 3 μ\muμ G and Having Equal but Opposite Charges of Magnitude of Having

Two Particles,each Having a Mass of 3 $\mu$ G and Having Equal but Opposite Charges of Magnitude of Having