A small plastic ball of mass 6.10 10^3 kg and charge +0.150 µC is suspended from an insulating thread and hangs between the plates of a capacitor. The ball is in equilibrium, with the thread making an angle of 30.0° with respect to the vertical. The area of each plate is 0.0150 m2. What is the magnitude of the charge on each plate?
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Draw the vector diagram. The vertical force on the ball is mg. The horizontal force must then be mg*tan30. That horizontal force must equal electrostatic force Eq where E is the electric field in the capacitor. E=charge/area*epsilon
solve for charge.
To find the magnitude of the charge on each plate, we can use the conditions of equilibrium for the suspended ball. The force acting on the ball must be balanced, so we need to consider both the gravitational force and the electrostatic force.
Let's start by considering the gravitational force on the ball. The force of gravity pulling the ball downwards can be calculated using the formula:
F_gravity = m * g
where m is the mass of the ball and g is the acceleration due to gravity (approximately 9.8 m/s²).
Given m = 6.10 * 10^(-3) kg, we can calculate F_gravity:
F_gravity = (6.10 * 10^(-3) kg) * (9.8 m/s²)
Now, let's consider the electrostatic force acting on the ball. The electrostatic force experienced by the ball is given by:
F_electrostatic = q * E
where q is the charge on the ball and E is the electric field between the plates of the capacitor.
In equilibrium, the electrostatic force must balance the force of gravity. This means:
F_electrostatic = F_gravity
Substituting the formulas for every force, we get:
q * E = m * g
Now, we can solve for the electric field E:
E = (m * g) / q
Given that m = 6.10 * 10^(-3) kg, g = 9.8 m/s², and q = 0.150 µC (which is equivalent to 0.150 * 10^(-6) C), we can calculate E:
E = ((6.10 * 10^(-3) kg) * (9.8 m/s²)) / (0.150 * 10^(-6) C)
Once we have the electric field E, we can calculate the magnitude of the charge on each plate by using the formula:
Q = E * A
where Q is the magnitude of the charge on each plate and A is the area of each plate.
Given that A = 0.0150 m², we can calculate Q:
Q = E * A
Now you have all the information you need to calculate the magnitude of the charge on each plate.