Question

One possible way of levitating (floating) an object might be to use the forces associated with charged objects. For example, suppose you have two charged spheres (qA and qB) of negligible mass fixed 0.50 m apart on a vertical pole. The lower of the spheres (qB) carries a fixed charge of -3 uC, and the upper one (qA) carries a charge that can be adjusted. A 30 g sphere carrying a charge qC = +8 uC can move freely on the pole below the other two. You want to levitate (float) the massive sphere (qC) 1.0 m below the 3 C sphere, as shown in the figure below. What should the charge on the upper sphere (qA) be adjusted to in order to achieve this task?

0.5 m 1.0 m

Answer 1

Q_A = ? q_B = -30 mu c m_c = 30 g = 0.03 kg q_A is assumed negative hence force will be upward. F_A and F_B are electrons total coulomb forces m_c g = F_A + F_B 0.03 times 9.8 = kq_A q_C/1.5^2 + kq_B q_C/1^2 0.03 times 9.8 = 9 times 10^9 times 8 times 10^-6 ( Vertical-bar q_A Vertical-bar /1.5^2 + 3 times 10^-6/1^2) 4.083 times 10^-6 = Vertical-bar q_A Vertical-bar /1.5^2 + 3 times 10^-6/1^2 Vertical-bar q_A Vertical-bar = 2.4375 times 10^-6 C q_A = -2.4375 mu C