Solving Gauss's Law Problem: Excess Electrons in Plastic Sphere

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SUMMARY

The problem involves calculating the number of excess electrons required to create an electric field of 1250 N/C just outside a plastic sphere with a diameter of 23.0 cm. Using the equation E = Q / (4 * π * ε * r²), the charge was initially calculated as 7.353 x 10^-9 C. Upon dividing this charge by the elementary charge (1.602 x 10^-19 C), the result was approximately 45,904,610,632 electrons. The error arose from using the diameter instead of the radius in the calculations.

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Homework Statement



How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 23.0cm in diameter to produce an electric field of 1250N/C just outside the surface of the sphere?

Homework Equations



E=Q/4*pi*ε*r^2


The Attempt at a Solution



I've attempted to find the charge using that equation and got 7.353*10^-9. Then to find the number of electrons I did 7.353*10^-9/1.602*10^-19 and I get 45904610632 electrons. It keeps saying I am wrong and I can't figure out why. Can anyone please tell me if I am doing something wrong.

Thanks
 
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NEVERMIND. They threw in 23cm as the diameter and not the radius...
 

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