Question

For the given graph between electric field $\left(E\right)$ and distance $\left(r\right)$ from axis of the infinite uniformly charged hollow cylinder, the outer radius of hollow cylinder is

• A. $0.5\text{m}$
• B. $1\text{m}$
• C. $1.5\text{m}$
• D. $2\text{m}$

Answer 1

The correct option is B $1\text{m}$

Given that,
$r=$ Distance from axis of cylinder
Let the radius of the cylinder is $R$ and $E_r$ is the electric field at distance $r$ from the axis of the cylinder.
Case I: When $r>R$
$E_{r>R}=\frac{\sigma R}{{ϵ}_{0}r}$
($\sigma =$Surface charge density)

Case II: When $r=R$
$E_{r=R}=\frac{\sigma R}{{ϵ}_{0}r}=\frac{\sigma }{{ϵ}_0}$

Case III: When $r<R$
$E_{r<R}=0$

For any infinite uniformly charged hollow cylinder, the electric field in the region inside the cylinder is zero and at points just outside the cylinder is maximum and it decreases as distance from the axis increases.
From graph, we can see that at $r=1\text{m}$, electric field is maximum. Thus, the radius of infinite uniformly charged hollow cylinder is $R=1\text{m}$.