Discussion Forum



1)

Let E1(r), E2(r) and E3(r)  be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge density   $\sigma$.If   $E_{1}(r_{0})=E_{2}(r_{0})=E_{3}(r_{0})$    at a  given distance r0 , then

   


A) $Q=4\sigma\pi r_0^2$

B) $r_{0}=\frac{\lambda}{2\pi\sigma}$

C) $E_{1}\left(\frac{r_{0}}{2}\right)=2E_{2}\left(\frac{r_{0}}{2}\right)$

D) $E_{2}\left(\frac{r_{0}}{2}\right)=2E_{3}\left(\frac{r_{0}}{2}\right)$

Answer:

Option C

Explanation:

$\frac{Q}{4\pi \epsilon_{0}r_0^2}=\frac{\lambda}{2\pi \epsilon_{0}r_{0}}=\frac{\sigma}{2\epsilon_{0}}$

                          $Q=2\pi \sigma r_0^2$

 (a) is incorrect,   $r_{0}=\frac{\lambda}{\pi\sigma}$

   (b)    is incorrect,   $E_{1}(\frac{r_{0}}{2})=4E_{1}(r_{0})$

 As,            $E_{1}\propto\frac{1}{r^{2}}$

    $E_{2}\left(\frac{r_{0}}{2}\right)=2E_{2}(r_{0})$     as    $E_{2}\propto\frac{1}{r}$

$\Rightarrow  $  (c) is correct.

    $E_{3}\left(\frac{r_{0}}{2}\right)=E_{3}(r_{0})=E_{2}(r_{0})  $

 as          $E_{3}\propto r^{0}$

$\Rightarrow  $  (d) is in correct.