Question

An insulating solid sphere of radius $R$ has a uniform volume charge density and total charge $Q$. The plot of $V$ vs $x$ is hyperbolic in the region :

• A. $R>r$
• B. $r>R$
• C. throughout space
• D. never

Answer 1

The correct option is B $r>R$

For an insulating solid sphere of radius $R$ having total charge $Q$. The plot of $V$ vs $x$ is:

Inside the sphere $(x<R);V\left(x\right)=\frac{kQ}{2R}\left(\frac{3-r^2}{R^2}\right)$

On the sphere, $(x=R)$; $V\left(x\right)=\frac{kQ}{R}$

Outside the sphere, $(x>R),V\left(x\right)=\frac{kQ}{R}$

So, we see that outside $(x>R)$; $V\left(x\right)\propto \frac{1}{x}$

So, the curve is hyperbolic in the region $x>R$.