Calculate charge on object suspended between capacitor plates

[PoppletonPlace]

Homework Statement

It would be greatly appreciated if someone could check over my work. It is very likely that I made mistakes. If I made any mistakes, could you please tell me where I went wrong? Thank you. I will use this problem to study for my next exam. I have also attached a figure that I created that goes with this problem. Thanks again.

As shown in the Figure, a 30mg object with a charge q is suspended with a light string in a uniform electric field between the plates of a charged capacitor. The capacitance of the capacitor is 1mF, the separation between the parallel plates is 4.0cm and the charge (Q) on the capacitor is 1.25C. Calculate the charge q on the 30 mg object, when the suspension thread holding the charged object is in static equilibrium at an angle of 10 degrees with respect to the vertical.

C=1.0x10^-3 F
d= 4.0x10^-2 m
m= 30.0x10^-3 g
Q= 1.25C
θ= 10 degrees

Homework Equations

C=Q/V, E=V/s, q=FE

The Attempt at a Solution

ƩFx=0
ƩFy=0
Ty=mg
Tx=F

Ty=(30.0x10^-3g) * (9.8)
Ty= .294 N

cos(10)= .294N/T
T= .294N/.9848
T= .298535N

sin(10)=Tx/T
sin(10)=Tx/.2985
Tx=.05184N
Tx=F
F=.05184

C=Q/V
V=Q/C
V=1.25C/(1.0x10^-3F)
V=1.250x10^3V

E=V/s
E=(1.250x10^3V)/(4.0x10^4 m)
E= 3.125x10^4 v/m

q=F/E
q= .05184 N/ (3.125x10^4 v/m)
q= 1.658x10^-6 C

 

[gneill]

Check your conversion for mg to kg. Otherwise, your method looks okay.

 

[rude man]

Check your conversion for mg to kg. Otherwise, your method looks okay.

Looks like the OP used the correct magnitude for mass, he/she just used g instead of kg for the unit designator.

 

[gneill]

Looks like the OP used the correct magnitude for mass, he/she just used g instead of kg for the unit designator.

Perhaps, but the resulting order of magnitude of the y-component of the tension, Ty, is incorrect.

 

[rude man]

Perhaps, but the resulting order of magnitude of the y-component of the tension, Ty, is incorrect.

Why? Ty = mg = 30e-3 * 9.8 = 0.294N.

 

[gneill]

Why? Ty = mg = 30e-3 * 9.8 = 0.294N.

30mg = 30 x 10^-3 grams = 30 x 10^-3 x 10^-3 kg = 3.0 x 10^-5 kg

30mg x g = ?

 

[rude man]

30mg = 30 x 10^-3 grams = 30 x 10^-3 x 10^-3 kg = 3.0 x 10^-5 kg

30mg x g = ?

Right you are. That is a mighty light mass! I was thinking 30g, obviously. Thanks.