Question

A small plastic ball with a mass of 7.10 x 10⁻³ kg and with a charge of +0.161 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 0.0143 m². What is the magnitude of the charge on each plate?

Answer 1

`3.16097* 10^(-8)\ C`

Step-by-step explanation:

T = Tension on the string

E = Electric field

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

As the forces balance themselves we have the equations

`Tcos30=mg`

`Tsin30=Eq`

Dividing the equations we get

`tan30=(Eq)/(mg)\\\Rightarrow E=(mgtan30)/(q)\\\Rightarrow E=(7.1* 10^(-3)* 9.81tan30)/(0.161* 10^(-6))\\\Rightarrow E=249770.33291\ N/C`

Electric field is given by

`E=(Q)/(A\epsilon)\\\Rightarrow Q=EA\epsilon\\\Rightarrow Q=249770.33291* 0.0143* 8.85* 10^(-12)\\\Rightarrow Q=3.16097* 10^(-8)\ C`

The magnitude of the charge on each plate is
`3.16097* 10^(-8)\ C`