Respuesta :
Answer:
1) [tex]\rm q_2[/tex] is positive.
2) [tex]\rm q_2=4.56\times 10^{-10}\ C.[/tex]
Explanation:
Part 1:
The charged rod is held above the balloon and the weight of the balloon acts in downwards direction. To balance the weight of the balloon, the force on the balloon due to the rod must be directed along the upwards direction, which is only possible when the rod exerts an attractive force on the balloon and the electrostatic force on the balloon due to the rod is attractive when the polarities of the charge on the two are different.
Thus, In order for this to occur, the polarity of charge on the rod must be positive, i.e., [tex]\rm q_2[/tex] is positive.
Part 2:
Given:
- Mass of the balloon, m = 0.00275 kg.
- Charge on the balloon, [tex]\rm q_1 = -3.50\times 10^{-8}\ C.[/tex]
- Distance between the rod and the balloon, d = 0.0640 m.
- Acceleration due to gravity, [tex]\rm g = 9.81\ m/s^2.[/tex]
In order to balloon to be float in air, the weight of the balloom must be balanced with the electrostatic force on the balloon due to rod.
Weight of the balloon, [tex]\rm W = mg = 0.00275\times 9.81=2.70\times 10^{-2}\ N.[/tex]
The magnitude of the electrostatic force on the balloon due to the rod is given by
[tex]\rm F_e = \dfrac{1}{4\pi \epsilon_o}\dfrac{|q_1||q_2|}{d^2}.[/tex]
[tex]\rm \dfrac{1}{4\pi \epsilon_o}[/tex] is the Coulomb's constant.
For the elecric force and the weight to be balanced,
[tex]\rm F_e = W\\\dfrac{1}{4\pi \epsilon_o}\dfrac{|q_1||q_2|}{d^2}=W\\8.99\times 10^9\times \dfrac{3.50\times10^{-8}\times |q_2| }{0.0640^2}=2.70\times 10^{-2}\\|q_2| = \dfrac{2.70\times 10^{-2}\times 0.00640^2}{8.99\times 10^9\times 2.70\times 10^{-7}}=4.56\times 10^{-10}\ C.[/tex]
