Question

Charge Q = 8.00 μC is distributed uniformly over the volume of an insulating sphere that has radius R = 12.0 cm . A small sphere with charge q=+3.00 μC and mass 6.00.×10−5kg is projected toward the center of the large sphere from an initial large distance. The large sphere is held at a fixed position and the small sphere can be treated as a point charge.

What minimum speed must the small sphere have in order to come within 9.00 cm of the surface of the large sphere?

Express your answer with the appropriate units.

Answer 1

Q=8.00µC & q= 3.00µC

R=12.0cm =0.12m, m=6.00*10^-5 kg

r=9.00cm = 0.09 m

Use law of conservation of energy,

KE_i+PE_i = KE_f +PE_f

1/2mv_i² + kQq/d_i = 1/2mv_f² + kQq/d_f

1/2mv_i² - 1/2mv_f² = kQq/d_f - kQq/d_i

1/2m(v_i² - v_f²) = kQq(1/d_f - 1/d_i)

Finally the sphere stops at a distance 9.00cm from the large sphere hence, v_f = 0 m/s

Initial distance is too large. Hence d_i = infinity

d_f = R +r = 12.00cm +9.00cm = 21.00cm = 0.21m

Plugging all values in above eqn,

½*6.00*10^-5*(v_i² - 0²) = (9*10^9*8.00*10^-6*3.00*10^-6)*(1/0.21 – 1/infinity)

v_i= 185.16 m/s