Jacobian Matrix

Electric field on the surface of a Spherical Shell

Two spherical shells of same surface charge density but the radius in the ratio 1: 2 What is the ratio of electric fields on the surface of the spherical shell

E=(1/4πε₀)q/r²

On the surface of the sphere r=R (radius of the shell)

•^•• E=(1/4πε₀)q/R²

But q=σA (σ=surface charge density and A=surface area=4πR²)

•^•• E=(1/4πε₀) σ 4πR²/R²

 ie E=σ/ ε₀

On the surface of the shell, E is independent of radius of the shell but depends  on the surface charge density

In this case the surface charge density is the same so ratio of E on the surface is 1: 1

Prepared by Sai’s Classes Poonkunnam Thrissur +919846088761