Two identical particles,each with a mass of 4.5 $\mu$g and a charge of 30 nC,are moving directly toward each other with equal speeds of 4.0 m/s at an instant when the distance separating the two is equal to 25 cm.How far apart will they be when closest to one another?
A)9.8 cm
B)12 cm
C)7.8 cm
D)15 cm
E)20 cm

Question

Quizplus · Accepted Answer

Using conservation of energy, the kinetic energy at any point is equal to the potential energy due to the electrostatic force between the two particles. Therefore,

1/2mv^2 = kq^2/r

where m is the mass of one particle, v is the speed of each particle, q is the charge on each particle, k is Coulomb's constant, and r is the distance between the particles. Solving for r when the particles are closest to each other,

r = kq^2/mv^2

Plugging in the given values,

r = (9 × 10^9 Nm^2/C^2)(30 × 10^-9 C)^2/(2 × 4.5 × 10^-3 kg)(4.0 m/s)^2

r ≈ 0.078 m = 7.8 cm

Therefore, the particles will be closest to each other when they are 7.8 cm apart. The answer is (C).

Two Identical Particles,each with a Mass of 4 μ\muμ G and a Charge of 30 NC,are Moving Directly Toward

Two Identical Particles,each with a Mass of 4 $\mu$ G and a Charge of 30 NC,are Moving Directly Toward