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

Answer:

the magnitude of the charge Q on each plate is $3.053 *10^{-8} \ C$

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;

$tan \ \theta = \frac{Eq}{mg}$    ----- equation (1)

Also by using Gauss Law ;

$Q = \epsilon_0 \phi$

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

Combination equation 1 and 2 together ; we have

$Q = \frac{\epsilon_0\ * \ m\ *\ g \ \ * \ tan \theta \ * \ A}{q}$

$Q = \frac{(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}$

$Q = 3.053 *10^{-8} \ C$