Question

A small plastic ball with a mass of 7.00 10-3 kg and with a charge of +0.155 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 0.0135 m2. What is the magnitude of the charge on each plate?

Answer 1

the magnitude of the charge Q on each plate is
`3.053 *10^(-8) \ C`

Step-by-step explanation:

Given that :

mass (m) =
`7.00 *10 ^(-3) \ kg`

charge (q) = +0.155 µC =
`+0.155 *10^(-6)\ C`

angle
`\theta = 30^0 \ C`

Area A on each plate = 0.0135 m²

From the diagram below;

`tan \ \theta = (Eq)/(mg)` ----- equation (1)

Also by using Gauss Law ;

`Q = \epsilon_0 \phi`

`Q = \epsilon_0EA` ----- equation (2)

Combination equation 1 and 2 together ; we have

`Q = (\epsilon_0\ * \ m\ *\ g \ \ * \ tan \theta \ * \ A)/(q)`

`Q = ((8.85*10^(-12)C^2/N.m^2 )\ * \ (7.00*10^(-3) kg)\ *\ (9.8 m/s^2) \ \ * \ tan \(30 \ * \ (0.0135 m^2))/(0.155*10^(-6)\ C)`

`Q = 3.053 *10^(-8) \ C`