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Consider an electron and the spherical surface that encloses it in the figure below. Explain how the electric flux and electric field through this surface would change if the radius of surface were doubled.

flux and field

a. The flux would not change and the electric field would decrease by a factor of four.

b. The flux would decrease by a factor of two and the electric field would decrease by a factor of four.

c.The flux would decrease by a factor of four and the electric field would decrease by a factor of sixteen.

d. The flux would decrease by a factor of four and the electric field would not change.
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The flux according to Gauss Law $\phi=Q/\epsilon_0$

where Q is charge enclosed inside the body therefore flux will not change when the radius of surface is doubled because still the charge enclosed inside the body will be same.

Electric field at the surface$E = kQ/R^2$

therefore when the radius is doubled electric field will decrease by a factor of 4 . because now R' = 2R

==> $E' = kQ/(2R)^2=kQ/4R^2=E/4$

hence option (a) is correct i.e. The flux would not change and the electric field would decrease by a factor of four.

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