Question

Which of the following graph shows curve between electric field $\left(E\right)$ versus distance $\left(r\right)$ from infinite line charge having constant positive charge density.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

We know that, due to infinite line charge of constant linear charge density $\left(\lambda \right)$,

$E_{\text{II}}=0$ and $E_{\perp }=\frac{2k\lambda }{r}$

So, $E_{net}=\sqrt{E_{\text{II}}^2+E_{\perp }^2}=\frac{2k\lambda }{r}$

since, $k$ and $\lambda$ are constant.

$\Rightarrow E_{net}=\frac{\text{Constant}}{r}$

$\therefore E_{net}r=\text{constant}$

On taking $E_{net}$ at $y-$ axis and $r$ at $x-$ axis, we get

$xy=\text{constant}$

This is the equation of rectangular hyperbola.

Therefore, the curve between $E$ and $r$ is a rectangular hyperbola.

Hence, option $\left(d\right)$ is correct.