Question
Consider a thin spherical shell of radius $$R$$ with centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $$\left| {\vec E\left( r \right)} \right|$$ and the electric potential $$V\left( r \right)$$ with the distance $$r$$ from the centre, is best represented by which graph?
A.
B.
C.
D.
Answer :
Solution :
For a thin uniformly positive charged spherical shell
(i) Inside the shell at any point
$$E = 0\,{\text{and}}\,V = \frac{1}{{4\pi { \in _0}}}\frac{q}{R} = constt.$$
where $$q =$$ charge on sphere
$$R =$$ Radius of sphere
(ii) Outside the shell at any point at any distance $$r$$ from the centre $$E \propto \frac{1}{{{r^2}}}\,{\text{and}}\,V \propto \frac{1}{r}$$
For a thin uniformly positive charged spherical shell
(i) Inside the shell at any point
$$E = 0\,{\text{and}}\,V = \frac{1}{{4\pi { \in _0}}}\frac{q}{R} = constt.$$
where $$q =$$ charge on sphere
$$R =$$ Radius of sphere
(ii) Outside the shell at any point at any distance $$r$$ from the centre $$E \propto \frac{1}{{{r^2}}}\,{\text{and}}\,V \propto \frac{1}{r}$$
