The magnitudes of the charges on two identical small metal spheres are in the ratio 5:1 .The Coulomb interaction force between them is F1.If they are brought into contact and then separated to their respective original positions,the Coulomb interaction force between them becomes F2.Which of the following is/are possible magnitude ratios of F1:F2 ?
(1)5:9
(2)5:4
(3)5:2
A.(1)only
B.(3)only
C.(1)and(2)only
D.(2)and(3)only
答案係C,請高手賜教！！點解會係C ??? T_T
Phy HKALE 2003 MC
2013-01-20 7:00 pm
回答 (2)
2013-01-20 8:13 pm
✔ 最佳答案
Let q be the charge on a sphere. Then the charge on the other sphere is 5qHence, F1 = k(5q).(q)/r^2 = 5kq^2/r^2
where k is the electrostatic constant, and r is their separation.
Assume that the charges on the two spheres are of the same sign. When they are brought into contact and then separated, charges are equally shared between the two spheres. The charge on each sphere is thus (5q+q)/2 = 3q
Hence, F2 = k(3q).(3q)/r^2 = 9kq^2/r^2
F1/F2 = 5/9 = 5:9
Assume that the charges on the two spheres are of opposite sign. When they are brought into contact and then separated, charges are equally shared between the two spheres. The charge on each sphere is thus (5q-q)/2 = 2q
Hence, F2 = k(2q).(2q)/r^2 = 4kq^2/r^2
Thus, F1/F2 = 5/4 = 5: 4
The answer is thus option C.
2013-01-20 9:32 pm
option C is the answer.^^
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