Let E_1(r), E_2(r) and E_3(r) be the respective electric fields a… - Vidyadip

MCQ

Let $E_1(r), E_2(r)$ and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$, an infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $\sigma$. if $E_1\left(r_0\right)=E_2\left(r_0\right)=E_3\left(r_0\right)$ at a given distance $r_0$, then

A
$Q =4 \sigma \pi r_0^2$
B
$r_0=\frac{\lambda}{2 \pi \sigma}$
✓
$E_1\left(r_0 / 2\right)=2 E_2\left(r_0 / 2\right)$
D
$E_2\left(r_0 / 2\right)=4 E_3\left(r_0 / 2\right)$

✓

Answer

Correct option: C.

$E_1\left(r_0 / 2\right)=2 E_2\left(r_0 / 2\right)$

c
$\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 $ $\quad$$A$ incorrect

$r_0=\frac{\lambda}{\pi \sigma} $ $\quad$$B$ incorrect

$E_1\left(\frac{r_0}{2}\right)=\frac{4 E_1\left(r_0\right)}{1} $

$E_2\left(\frac{r_0}{2}\right)=2 E_2\left(r_0\right) \Rightarrow $ $\quad$$C$ correct

$E_3\left(\frac{r_0}{2}\right)=E_3\left(r_0\right)=E_2\left(r_0\right)$ $\quad$$D$ incorrect

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