A small plastic ball with a mass of 7.00 10-3 kg and with a charge of +0.162 µC is suspended from an insulating thread and hangs between the plates of a capacitor (see the drawing). 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 0.0145 m2. What is the magnitude of the charge on each plate?
The portion of weight opposing the electric force is mg*tanTheta, right? Set that equal to the electric force.
(If you don't see the force, then draw the force diagram: mg downward, Fhorizontal. Fhorizontal =Eforce, but then Fhorizontal/mg=tanTheta, so Eforce=mgTanTheta
To find the magnitude of the charge on each plate of the capacitor, we can use the equilibrium condition of the ball hanging between the plates. Let's go step by step to calculate it.
1. First, let's calculate the weight of the plastic ball.
Weight = mass * gravity
= (7.00 * 10^-3 kg) * (9.8 m/s^2)
= 6.86 * 10^-2 N (Newtons)
2. Next, let's calculate the tension in the thread.
Tension = Weight / cos(angle)
= (6.86 * 10^-2 N) / cos(30.0°)
= 7.92 * 10^-2 N
3. Now, let's calculate the electric force acting on the ball.
Electric force = charge * electric field
= charge * (voltage / separation)
= charge * (V / d)
The given information does not directly provide the voltage (V) and separation (d) between the plates. Therefore, to proceed further, we need additional information about the capacitor or its electric field.
Please provide the voltage and separation between the plates (or any other relevant information) to calculate the magnitude of the charge on each plate.