A small plastic ball of mass 6.10 10^-3 kg and charge +0.150 µC?

Question

A small plastic ball of mass 6.10 10^-3 kg and charge +0.150 µC is suspended from an insulating thread and hangs between the plates of a capacitor. 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 0.0150 m2. What is the magnitude of the charge on each plate?

-----------------C

Answer 1

Given:

0.150 microcoulombs = 1.5*10^-7 C

eo=8.854*10^-12

A=0.0150 m^2

m=6.10*10^-3 kg

thread @30 with vertical

g=9.8

The ball is in equilibrium: all vectors cancel

m*g=T*Cos(30)

solve for T

T=m*g/Cos(30)

T=((6.1*10^-3)*9.8)/0.866

= 6.903*10^-2 n

*********************************

E*q=T*Sin(30)

solve for E

E=T*Sin(30)/q

E=((6.903*10^-2)*(0.499)

/(1.5*10^-7)

E= 229639.8 n/c

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E for parallel plate capacitor

E=Q/(A*eo)=229639.8  n/c

Q=E*A*eo

Charge on plates:

Q=(229639.8 *0.0150)*(8.854*10^-12)

= 3.0498*10^-8 C "answer"

or

3.0498 *10^-8 C = 0.030498 uC