The net electric flux due to the net charge enclosed by a surface is given by Ф= q/ E (Gauss Theorem) . The electric flux due to a unit charge is given by Φ= q/E . What encloses this charge according to Gauss theorem? Is the space around this free charge which encloses it a Gaussian surface? Can earth / surrounding be considered as a Gaussian surface enclosing this charge? What will be the flux if a unit positive charge is enclosed by earth and space and the charge is placed at the Earth's atmosphere? What will be the value of E in this case?. Justify your answer in detail.
Answers
Answer:
Electric Flux through a surface is defined as the surface integral of the electric field lines passing normally through the surface.
ϕ=∫
E
.
dS
According to gauss's law, total electric flux through a closed surface equals the net charge enclosed in the surface divided by the permittivitty.
Consider a point charge q. Its net electric flux through any closed surface enlcosing it will be be equal to ϕ=
ε
o
q
. This is independent of the choice of the shape and size of the closed surface.
The SI unit of electric flux is Volt - metres (V m)
(b)
For charged spherical shell, all charge lies on the outer circumference of the surface.
Consider a charged spherical shell with outer radius b and inner radius a. The charge resides at a radius b from the centre. Consider a gaussian surface of radius a<r<b. Charge enclosed in this guassian surface will be zero.
Using gauss's law,
∫E.ds=
ε
o
q
enclosed
E×2πrdr=0
E=