Question

Select the correct alternative : A non-conducting solid sphere of $R$ is uniformly charged. The magitude of the electric field due to the sphere at a distance $r$ from its centre:

• A. increases as r increases, for $r<R$
• B. decreases as $r$ increases, for $0<r<\infty$
• C. decreases as $r$ increases, for $R<r<\infty$
• D. is discontinuous at $r=R$

Answer 1

Answer: (A), (C)

The correct options are
A increases as r increases, for $r<R$
C decreases as $r$ increases, for $R<r<\infty$

Using Gauss's law , field inside the sphere , $E_{in}.4\pi r^2=\frac{\rho .\frac{4}{3}\pi r^3}{{ϵ}_0}\Rightarrow E_{in}=\frac{\rho r}{3{ϵ}_0}$

outside the sphere, $E_{out}.4\pi r^2=\frac{\rho .\frac{4}{3}\pi R^3}{{ϵ}_0}\Rightarrow E_{out}=\frac{\rho R^3}{3{ϵ}_0{r}^2}$

Ans:(A),(C)