Suspending a -3nC charge in an electric field

[MathGnome]

Here's the question:
What are the strength and direction of an electric field that will balance the weight of a 1.0g plastic sphere that has been charged to -3.0nC?

Ok, here's what I did.

Knowns
q = -3nC
m = 1.0g
weight force = 9.8 gm/s^2 (I assume this is done on surface of earth)

Now, here's the calculations I did:
Since I need .0098 N/Kg to balance the plastic sphere, I use the equation
(.001Kg)(.0098 N/Kg) which shows that I need at least 1x10^-5 N to overcome the force of gravity on the sphere. So, I know that the plastic sphere has a charge of -3nC and I need at least 1x10^-5 N to overcome it's weight. So, using (1.0x10^-5 N ) / (3x10^-9 C) I find that I will need a force of about 3333 N/C on the plastic sphere. Since the charge on the plastic sphere is negative, I will say the electric field's direction needs to be downward (sames repell).

The book agrees with my direction, but says that I will need a force of at least 3.27x10^6 N/C

I know it's probably an error in my math, but I just can't seem to find it.


Thanks for any help,
MathGnome

 

[Galileo]

Knowns
q = -3nC
m = 1.0g
weight force = 9.8 gm/s^2 (I assume this is done on surface of earth)

Now, here's the calculations I did:
Since I need .0098 N/Kg to balance the plastic sphere, I use the equation
(.001Kg)(.0098 N/Kg) which shows that I need at least 1x10^-5 N to overcome the force of gravity on the sphere.

Your complicated way of doing prevents you from seeing what you are actually doing. You said the 'weight force' (the gravitational force on the sphere, from F=mg) is 9.8 gm/s^2. That's okay, but then you say you need 0.0098N/kg to balance the sphere!?
No, you need 9.8 gm/s^2=9.8 x 10^-3 N to balance the gravitational force. (Or did you mean 9.8 x 10^-3 N/g ?) You already calculated the necessary force, so by doing this you're going in circles.

Here's some problem solving advice that will pay dividends. Solve this question generally, using symbols. The gravitational force pulling the sphere down is F=mg. The electric force pushing it up is F=qE, these are both magnitudes. Therefore, to balance they must be equal in magnitude: mg=qE. Solve for E, since that's what you're looking for and IN THE END, enter your numerical values.

 

[MathGnome]

Ahh, thanks.. I have a problem where I can't concentrate and I'm usually thinking about 3 things at once when I'm doing a problem, so I usually overcomplicate things

Thanks for the help on this problem. Does anyone know a good trick to concentrate? I notice that if I drink coffee I can visualize the problem and solve it easily, but if I'm just doing it normally I end up thinking about a lot of tangent ideas and end up not able to focus on all of them at once.

 

[Galileo]

Lot's of practice is the key really.