Question #2528

Three identical small spheres weighing 0.1 g are suspended from a point with silky thread of length 20 cm each. What charges in e.s.u should be imported to the spheres, so that each thread makes an angle of 30o with the vertical. Assume the charges are to be equal.

Expert's answer

Let m = 0.1g be the mass of each spheres,

l = 20cm be length of each thread

q be the charge of each sphere.

Since the angle between threads is 2*30 = 60, it follows that the distance between these spheres is equal to l=20cm.

There are three forces acting on each of the spheres:

1) Gravitational force, P=mg

2) Tension of thread, N

3) Coulomb's force, F= q^{2}/l^{2}Since the spheres do not move, the sum of these forces is zero,

P + N + F = 0

Projecting this vector equation to the horisontal axis we get that

mg tan 30 = q^{2}/l^{2}Hence

q = l * √{ mg /√{3} } = 20cm * √{ 0.1g * 980 cm/s^{2} / 1,73 } = 150,44 e.s.u

l = 20cm be length of each thread

q be the charge of each sphere.

Since the angle between threads is 2*30 = 60, it follows that the distance between these spheres is equal to l=20cm.

There are three forces acting on each of the spheres:

1) Gravitational force, P=mg

2) Tension of thread, N

3) Coulomb's force, F= q

P + N + F = 0

Projecting this vector equation to the horisontal axis we get that

mg tan 30 = q

q = l * √{ mg /√{3} } = 20cm * √{ 0.1g * 980 cm/s

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