Charge Q = 7.00 C is distributed uniformly over the volume of an insulating sphe
ID: 1600204 • Letter: C
Question
Charge Q = 7.00 C is distributed uniformly over the volume of an insulating sphere that has radius R = 13.0 cm . A small sphere with charge q=+ 1.00 C and mass 6.00.×105kg 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. Part A What minimum speed must the small sphere have in order to come within 5.00 cm of the surface of the large sphere? Express your answer with the appropriate units. v =
Explanation / Answer
Concept used : Net Work done = change in kinetic energy
W = Work done to bring a point charge q from large distance to a distance r from centre of a charged sphere = q V
V= potential of that point due to sphere
In our case we have
q = 1 *10-6 C
V =kQ/r
(Q = 7 * 10-6 C , r = 13+5 =18 cm = 0.18 m )
V = 9 * 109 * 7 *10-6/ 0.18 = 3.5 * 105 V
so W = qV = 1 *10-6 * 3.5 * 105 = 0.35 J
Let initial speed given be v
final speed at 18 cm from centre of big sphere = 0 ( as we want minimum speed )
so
kinetic energy change of small sphere = mv2/2 - 0 = 6*10-5 * v2/2 =3 * 10-5 v2
3 * 10-5 v2 = W
3 * 10-5 v2 = 0.35
v2 = 1.167 * 10-6
v = 1.08 * 10-3 m/s