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

Answer:

$3.16097\times 10^{-8}\ C$

Explanation:

T = Tension on the string

E = Electric field

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

As the forces balance themselves we have the equations

$Tcos30=mg$

$Tsin30=Eq$

Dividing the equations we get

$tan30=\dfrac{Eq}{mg}\\\Rightarrow E=\dfrac{mgtan30}{q}\\\Rightarrow E=\dfrac{7.1\times 10^{-3}\times 9.81tan30}{0.161\times 10^{-6}}\\\Rightarrow E=249770.33291\ N/C$

Electric field is given by

$E=\dfrac{Q}{A\epsilon}\\\Rightarrow Q=EA\epsilon\\\Rightarrow Q=249770.33291\times 0.0143\times 8.85\times 10^{-12}\\\Rightarrow Q=3.16097\times 10^{-8}\ C$

The magnitude of the charge on each plate is $3.16097\times 10^{-8}\ C$