Gauss's Law: I need to check this answer

[DivGradCurl]

A conducting sphere of radius $$10 \mbox{ cm}$$ has an unknown charge. If the electric field $$17 \mbox{ cm}$$ from the center of the sphere has the magnitude $$3.2 \times 10 ^3 \mbox{N/C}$$ and is directed radially inward, what is the net charge on the sphere?

Let:

$$R = 10 \mbox{ cm}$$

$$r = 17 \mbox{ cm}$$

Gauss's Law:

$$Q _{\mbox{Enc}} = \epsilon _0 \Phi = \epsilon _0 \oint \vec{E} \cdot d\vec{A} = -\epsilon _0 EA = -\epsilon _0 E \left( 4 \pi r^2 \right) \approx -3.6 \times 10^{-9} \mbox{ C}$$

Is there anything wrong here? I am not sure.

Any help is highly appreciated.​

 

[quantumdude]

I don't have a calculator handy so I can't comment on your numerical answer, but all your other steps are fine.

 

[quicknote]

Thank you.

I can confirm that your application of Gauss's Law is correct. The equation you have used is the integral form of Gauss's Law, which relates the net charge enclosed within a closed surface to the electric flux through that surface. By setting the electric flux equal to the given electric field multiplied by the surface area of the sphere, you have correctly solved for the net charge on the sphere. Your final answer of -3.6 \times 10^{-9} \mbox{ C} indicates that the sphere has a net negative charge of this magnitude. I do not see any errors in your calculation, but it is always a good practice to double check your work to ensure accuracy. Great job!