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Electrostatics question

2014 · Shift 1 · Q43

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JEE Advanced
Physics
Electrostatics
2014 · Shift 1 · Q43

Electrostatics question

2014 · Shift 1 · Q43

JEE AdvancedPhysicsElectrostaticsMultiple correct+3 / −1

Let

{E_1}\left( r \right),{E_2}\left( r \right)

and

{E_3}\left( r \right)

be the respective electric field 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
${r_0} = {\lambda \over {2\pi \sigma }}$
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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