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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

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# Suspending a -3nC charge in an electric field

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