If the electric flux through a closed surface is zero, is the electric field necessarily zero at all points on the surface? Explain. What about the converse: If E → = 0 at all points on the surface is the flux through the surface zero?
If the electric flux through a closed surface is zero, is the electric field necessarily zero at all points on the surface? Explain. What about the converse: If E → = 0 at all points on the surface is the flux through the surface zero?
If the electric flux through a closed surface is zero, is the electric field necessarily zero at all points on the surface? Explain. What about the converse: If
E
→
=
0
at all points on the surface is the flux through the surface zero?
Expert Solution & Answer
To determine
Check whether zero electric flux means zero electric filed at every point on surface and vice versa
Answer to Problem 1Q
No. Zero electric flux do not imply zero electric fled at all points on surface.
Yes. Zero electric field at all points on surface means the zero electric flux.
Explanation of Solution
Electric flux is the measure of number of electric filed lines passing through the surface. According to Gauss’s theorem, zero electric flux over a surface means that the net charge enclosed by the surface is zero. But the electric filed can be nonzero by the charges lies inside or outside the Gaussian surface.
Net electric field over a surface can be zero if electric field is pointing inwards at some points and outwards from the surface at some other points. If the electric field is zero, it is no electric flux and by Gauss’ theorem there will be not net charge.
Therefore, it is incorrect that to say zero electric flux do not imply zero electric fled at all points on surface and it is correct that zero electric field at all points on surface implies the zero electric flux.
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A certain region of space bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface?
Calculate the absolute value of the electric flux for the following situations (In all case provide your answer in N m2/C):
c. A uniform electric field E = (−350 i + 350 j + 350 k) N/C through a disk of radius 3 cm in the x-z plane.
The figure shows a sphere carrying a uniformly distributed volume charge Q. Three Gaussian surfaces are concentric with the sphere as shown.
a)Which Gaussian surface(s) has the greatest electric flux though it?
b)On which of Gaussian surface is the electric field the greatest?
Chapter 22 Solutions
Physics for Scientists and Engineers with Modern Physics
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