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
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
- [IIT 2014]
- A
$Q =4 \sigma \pi r_0^2$
- B
$r_0=\frac{\lambda}{2 \pi \sigma}$
- C
$E_1\left(r_0 / 2\right)=2 E_2\left(r_0 / 2\right)$
- D
$E_2\left(r_0 / 2\right)=4 E_3\left(r_0 / 2\right)$
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Figure:$Image$
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$(A)$ independent of a
$(B)$ directly proportional to a
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$(D)$ inversely proportional to a
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