# Gauss's Law: I need to check this answer

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.

## Answers and Replies

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Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
I don't have a calculator handy so I can't comment on your numerical answer, but all your other steps are fine.