Question

A charge of 21.0 μC is held fixed at the origin.

A. If a -6.00 μC charge with a mass of 3.90 g is released from rest at the position (0.925 m, 1.17 m), what is its speed when it is halfway to the origin?

B.Suppose the -6.00 μC charge is released from rest at the point x = 12(0.925m) and y = 12(1.17m). When it is halfway to the origin, is its speed greater than, less than, or equal to the speed found in part A?

C. Find the speed of the charge for the situation described in part B.

Answer 1

A)

Q₁ = charge at the origin = 21 x 10^-6 C

Q₂ = charge at the location (0.925, 1.17) = - 6 x 10^-6 C

r_i = initial distance between two charges = sqrt(0.925² + 1.17²) = 1.5 m

r_f = Final distance between two charges = 1.5/2 = 0.75 m

m = mass of the charge released = 3.90 x 10^-3 kg

Using conservation of energy

Initial potential energy = final potential energy at halfway + kinetic energy

k Q₁ Q₂/r_i = k Q₁ Q₂/r_f + (0.5) m v²

(9 x 10⁹) (21 x 10^-6) (- 6 x 10^-6)/(1.5) = (9 x 10⁹) (21 x 10^-6) (- 6 x 10^-6)/(0.75) + (0.5) (3.90 x 10^-3) v²

v = 19.7 m/s