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A thin spherical shell of radius R has a fixed charge +q distributed uniformly over its surface.Now the sphere's angular velocity increases linearly with time w = w0 + kt.The line integral of the electric field (∫E.dl ) around the circular path P located at the centre of the sphere is (Assume that the normal to the plane containing the path is along the +z axis and that the radius rp

A thin spherical shell of radius R has a fixed charge +q distributed uniformly over its surface.Now the sphere's angular velocity increases linearly with
time w = w0 + kt.The line integral of the electric field (∫E.dl ) around the circular path P located at the centre of the sphere is (Assume that the normal to the plane containing the path is along the +z axis and that the radius
rp

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Grade:12th Pass

1 Answers

Arun
25750 Points
4 years ago
Gauss's Law :   ∮Er​.dS=ϵo​qenclosed​​
As the charge lies on the surface of shell, thus no charge is enclosed by the Gaussian surface lying inside shell. Hence from Gauss's law, net electric field inside the shell is zero.
⟹   Er​=0   for  rR
Outside the shell :  r≥R
Charge enclosed by the Gaussian surface  qenclosed​=Q
From Gauss's law  Er​∮dS=ϵo​qenclosed​​
We get  Er​×4πr2=ϵo​Q​
Electric field at a point outside the shell  Er​=4πϵo​r2Q​  for r≥R
Thus electric field decreases as r21​

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