A small plastic ball with a mass of 6.50x10^-3 kg and with a charge of +0.150x10^-6 C is suspended from an insulating thread and hangs between the plates of a capacitor. The ball is in equilibrium, whit the tread making an angle of 30 degrees with respect to the vertical. The area of each plate is 0.0150 m^2. What is the magnitude of the charge of each plate?
Hey, look, posting the problem three times is not going to make me finish the managerial economics problem any faster :(
To find the magnitude of the charge on each plate, we need to use the concept of electric field and force on a charged object.
1. First, let's determine the force acting on the plastic ball. Since the ball is in equilibrium, the net force on it must be zero. The two forces acting on the ball are the gravitational force and the electric force.
2. The gravitational force can be calculated using the formula Fgravity = m * g, where m is the mass of the ball and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fgravity = (6.50x10^-3 kg) * (9.8 m/s^2) = 6.37x10^-2 N
3. Now, let's consider the electric force on the ball. The electric force can be calculated using the formula Felectric = q * E, where q is the charge on the ball and E is the electric field between the plates of the capacitor.
4. The ball is suspended in equilibrium, which means the electric force upward balances the gravitational force downward. Therefore, we can equate these forces:
Felectric = Fgravity
q * E = m * g
5. We can rearrange the equation to solve for the electric field E:
E = (m * g) / q
E = (6.50x10^-3 kg * 9.8 m/s^2) / (0.150x10^-6 C)
E = 4.2333x10^4 N/C
6. The electric field between the plates of the capacitor is equal to the electric field due to the charge on each plate. We can now calculate the magnitude of the charge on each plate.
E = V / d
Where V is the voltage between the plates and d is the distance between the plates.
7. The voltage can be calculated using the formula V = Ed:
V = (4.2333x10^4 N/C) * (d)
8. The distance between the plates is not given in the question. Without this information, we cannot determine the magnitude of the charge on each plate accurately.
To find the magnitude of the charge on each plate, we need to know the distance between the plates.